(original) (raw)

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y(Mo)q(dule)j(In)o(terconnection)g(Languages)f([14)o(,)f(5])g(and)h (notations)g(for)f(soft)o(w)o(are)f(arc)o(hitecture)i([15)o(,)g(4)o(,)g (9)o(,)37 2386 y(7,)g(6].)29 b(Although)19 b(it)f(is)h(commonly)g (understo)q(o)q(d)g(ho)o(w)f(to)f(simplify)j(system)e(structure)g(b)o (y)h(clustering)37 2442 y(comp)q(onen)o(ts,)c(there)f(is)h(little)g (consensus)g(on)f(ho)o(w)g(to)g(cluster)g(in)o(terconnections)i([13)o (])e(to)f(gain)i(a)f(similar)37 2499 y(simpli\014cation.)945 2640 y(2)p eop 3 2 bop 129 1145 a @beginspecial 35 @llx 184 @lly 576 @urx 607 @ury 3968 @rwi 2267 @rhi @setspecial % remember original state /origstate save def % build a temporary dictionary 20 dict begin % define space for color conversions /grays 1152 string def % space for gray scale line /npixls 0 def /rgbindx 0 def % lower left corner 35 184 translate % size of image (on paper, in 1/72inch coords) 541.44000 423.00000 scale % define 'colorimage' if it isn't defined % ('colortogray' and 'mergeprocs' come from xwd2ps % via xgrab) /colorimage where % do we know about 'colorimage'? { pop } % yes: pop off the 'dict' returned { % no: define one /colortogray { % define an RGB->I function /rgbdata exch store % call input 'rgbdata' rgbdata length 3 idiv /npixls exch store /rgbindx 0 store 0 1 npixls 1 sub { grays exch rgbdata rgbindx get 20 mul % Red rgbdata rgbindx 1 add get 32 mul % Green rgbdata rgbindx 2 add get 12 mul % Blue add add 64 idiv % I = .5G + .31R + .18B put /rgbindx rgbindx 3 add store } for grays 0 npixls getinterval } bind def % Utility procedure for colorimage operator. % This procedure takes two procedures off the % stack and merges them into a single procedure. /mergeprocs { % def dup length 3 -1 roll dup length dup 5 1 roll 3 -1 roll add array cvx dup 3 -1 roll 0 exch putinterval dup 4 2 roll putinterval } bind def /colorimage { % def pop pop % remove 'false 3' operands {colortogray} mergeprocs image } bind def } ifelse % end of 'false' case % define the colormap /cmap 12 string def % load up the colormap currentfile cmap readhexstring ffffff 000000 0000ff daa520 pop pop % lose return values from readhexstring % rlecmapimage expects to have 'w h bits matrix' on stack /rlecmapimage { /buffer 1 string def /rgbval 3 string def /block 384 string def % proc to read a block from file, and return RGB data { currentfile buffer readhexstring pop /bcount exch 0 get store bcount 128 ge { % it's a non-run block 0 1 bcount 128 sub { currentfile buffer readhexstring pop pop % look up value in color map /rgbval cmap buffer 0 get 3 mul 3 getinterval store % and put it in position i*3 in block block exch 3 mul rgbval putinterval } for block 0 bcount 127 sub 3 mul getinterval } { % else it's a run block currentfile buffer readhexstring pop pop % look up value in colormap /rgbval cmap buffer 0 get 3 mul 3 getinterval store 0 1 bcount { block exch 3 mul rgbval putinterval } for block 0 bcount 1 add 3 mul getinterval } ifelse } % end of proc false 3 colorimage } bind def 1152 900 8 % 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y(Before)k(pro)q(ceeding)i(with)f(the)f (formal)g(c)o(haracterization)h(of)e(tub)q(es)i(\(Section)g(3\),)f(the) g(description)37 1656 y(of)d(the)g(algorithms)g(for)f(clustering)j (soft)o(w)o(are)c(in)o(terconnections)j(\(Section)g(4\),)e(and)h(the)g (implications)i(of)37 1712 y(our)h(w)o(ork)f(regarding)h(future)g (researc)o(h)g(in)h(soft)o(w)o(are)d(structure)i(sp)q(eci\014cation)h (and)g(automatic)e(design)37 1769 y(extraction)21 b(\(Section)h(5\),)f (w)o(e)g(\014rst)g(giv)o(e)g(examples)h(of)e(comp)q(osite)h(comp)q (onen)o(ts)h(\(subsystems\))e(and)37 1825 y(comp)q(osite)c(in)o (terconnections)h(\(tub)q(es\).)37 1968 y Fo(2)67 b(Examples)23 b(of)f(Comp)r(osite)g(Comp)r(onen)n(ts)f(and)i(In)n(terconnections)37 2070 y Fp(Programs)14 b(are)g(structured)h(using)g(programming)g (language)g(comp)q(onen)o(ts)f(\()p Fn(e.g.,)h Fp(pro)q(cedures,)g (classes,)37 2126 y(mo)q(dules\))f(and)g(in)o(terconnections)g(\()p Fn(e.g.,)f Fp(calls,)h(imp)q(orts,)f(exp)q(orts,)g(inherits\).)20 b(Additional)15 b(structuring)37 2183 y(mec)o(hanisms)g(to)e(aggregate) g(programming)g(language)h(comp)q(onen)o(ts,)g(suc)o(h)g(as)g (subsystems,)f(ha)o(v)o(e)h(b)q(een)37 2239 y(used)f(for)e(some)h(time) g(no)o(w.)18 b(W)l(e)12 b(prop)q(ose)h(a)e(complemen)o(tary)h (structuring)g(mec)o(hanism)h(for)e(aggregating)37 2296 y(in)o(terconnections,)17 b(called)f(tub)q(es.)945 2640 y(3)p eop 4 3 bop 366 1601 a @beginspecial 104 @llx 156 @lly 506 @urx 633 @ury 2834 @rwi @setspecial 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 16 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.8 0 0 0.8 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -7.59035 -52.0482 ] concat Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 139.761 -231.952 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 10 0 0 1.40818 -1279.94 -119.9 ] concat %I 171 428 171 440 Line End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00235 0 0 1 141.023 54.6265 ] concat %I 4 124 435 178 435 297 435 331 414 4 MLine End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 138.808 75.6265 ] concat %I 4 126 422 172 422 300 422 336 433 4 MLine End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -24.9397 -96.506 ] concat Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg Blue 0 0 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 156.084 334.639 ] concat %I 71 500 121 530 Rect End Begin %I Line %I b 65535 3 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 156.084 329.639 ] concat %I 121 525 325 540 Line End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 247.084 854.639 ] concat %I [ (B) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg Green 0 1 0 SetCBg %I p 0 SetP %I t [ 1 0 0 1 415.084 354.639 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 506.084 874.639 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 415.084 314.639 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 506.084 834.639 ] concat %I [ (E) ] Text End Begin %I Line %I b 65535 3 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 156.084 299.639 ] concat %I 121 545 325 530 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 302.084 790.639 ] concat %I [ (\(1\) Module Interconnections) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 352.084 876.639 ] concat %I [ (import) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 351.084 833.639 ] concat %I [ (import) ] Text End End %I eop Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.13095 137.229 9.25465 ] concat %I 31 480 161 560 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 130.229 88.9156 ] concat %I 71 500 121 530 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.16667 386.478 -7.83425 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 222.229 607.916 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 173.229 634.916 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 533.229 638.916 ] concat %I [ (C) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 392.229 106.916 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 482.229 625.916 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg Blue 0 0 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 392.229 66.9156 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 483.229 586.916 ] concat %I [ (E) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 258.494 533.76 ] concat %I [ (\(2\) Adding subsystems and a tube) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.853986 0 0 1 150.977 175.916 ] concat %I 172 440 291 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.85441 0 0 1 151.285 156.916 ] concat %I 172 440 290 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 127.182 -117.662 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 10 0 0 1.40818 -1292.52 -5.61125 ] concat %I 171 428 171 440 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.5 242.229 418.916 ] concat %I 3 314 356 314 338 351 360 3 MLine End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.471591 242.229 430.216 ] concat %I 3 314 394 314 415 351 394 3 MLine End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00235 0 0 1 128.444 168.916 ] concat %I 4 124 435 178 435 297 435 331 414 4 MLine End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 126.229 189.916 ] concat %I 4 126 422 172 422 300 422 336 433 4 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 341.819 631.916 ] concat %I [ (tube) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -31.4458 -71.5662 ] concat Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg LtGray 0.762951 0.762951 0.762951 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.16667 419.659 -102.605 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 566.41 544.145 ] concat %I [ (C) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.853986 0 0 1 184.158 81.1446 ] concat %I 172 440 291 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.85441 0 0 1 184.466 62.1446 ] concat %I 172 440 290 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 160.363 -212.433 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 10 0 0 1.40818 -1259.34 -100.382 ] concat %I 171 428 171 440 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.5 275.41 324.145 ] concat %I 3 314 356 314 338 351 360 3 MLine End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.471591 275.41 335.445 ] concat %I 3 314 394 314 415 351 394 3 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 373.916 538.229 ] concat %I [ (tube) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg LtGray 0.762951 0.762951 0.762951 SetCFg %I cbg Red 1 0 0 SetCBg %I p 0 SetP %I t [ 1 0 0 1.13095 169.325 -83.3474 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 204.241 545.566 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 165.024 437.795 ] concat %I [ (\(3\) Using Subsystem Elision to Create Abstract Views of the Software Structure) ] Text End End %I eop Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 137.386 -233.566 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 229.386 285.434 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 180.386 312.434 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 540.386 316.434 ] concat %I [ (C) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 399.386 -215.566 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 489.386 303.434 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg Blue 0 0 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 399.386 -255.566 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 490.386 264.434 ] concat %I [ (E) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.853986 0 0 1 158.134 -146.566 ] concat %I 172 440 291 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.85441 0 0 1 158.442 -165.566 ] concat %I 172 440 290 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 134.339 -440.144 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 10 0 0 1.40818 -1285.36 -328.093 ] concat %I 171 428 171 440 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.5 249.386 96.4338 ] concat %I 3 314 356 314 338 351 360 3 MLine End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.471591 249.386 107.734 ] concat %I 3 314 394 314 415 351 394 3 MLine End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 348.976 309.434 ] concat %I [ (tube) ] Text End Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg LtGray 0.762951 0.762951 0.762951 SetCFg %I cbg Red 1 0 0 SetCBg %I p 0 SetP %I t [ 1.08434 0 0 1.08434 106.265 33.6145 ] concat %I 291 224 292 239 Rect End Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg LtGray 0.762951 0.762951 0.762951 SetCFg %I cbg Red 1 0 0 SetCBg %I p 0 SetP %I t [ 1.08434 0 0 1.08434 106.265 33.6145 ] concat %I 6 278 239 279 246 291 240 291 226 278 218 278 239 6 Poly End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.13095 144.386 -313.227 ] concat %I 31 480 161 560 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.16667 393.635 -330.316 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 140.736 211.82 ] concat %I [ (\(4\) Using Tube Elision to Create Abstract Views of the Software Structure) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -5.85541 -208.626 ] concat Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 139.761 -231.952 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 10 0 0 1.40818 -1279.94 -119.9 ] concat %I 171 428 171 440 Line End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.00235 0 0 1 141.023 54.6265 ] concat %I 4 124 435 178 435 297 435 331 414 4 MLine End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 138.808 75.6265 ] concat %I 4 126 422 172 422 300 422 336 433 4 MLine End End %I eop Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg LtGray 0.762951 0.762951 0.762951 SetCFg %I cbg Red 1 0 0 SetCBg %I p 0 SetP %I t [ 1.08434 0 0 1.08434 106.265 33.6145 ] concat %I 182 225 293 240 Rect End End %I eop showpage end @endspecial 449 1749 a Fp(Figure)16 b(2:)j Fm(Examples)f(of)f (Subsystems)f(and)i(T)l(ub)q(es)37 1887 y(A)o(tomic)g(Comp)q(onen)o(ts) f(and)h(In)o(terconnections)p 37 1902 966 2 v 37 1972 a Fp(The)13 b(\014rst)e(diagram)h(of)g(Figure)g(2)g(depicts)h(the)f (structure)g(of)f(a)h(simple)i(system,)d(at)h(the)g(lev)o(el)h(of)f (program-)37 2029 y(ming)17 b(language)f(constructs.)21 b(This)c(system)e(consists)h(of)g(three)g(mo)q(dules.)23 b(In)16 b(this)h(system,)e(mo)q(dule)i Fn(B)37 2085 y Fp(imp)q(orts)f(mo)q(dules)h Fn(D)f Fp(and)g Fn(E)p Fp(.)f(These)h(imp) q(orts)g(are)f(in)o(terconnections)i(that)e(enable)i(comp)q(onen)o(ts)f (in)g Fn(B)37 2142 y Fp(to)i(dep)q(end)i(on)e(exp)q(orted)h(comp)q (onen)o(ts)f(in)h Fn(D)g Fp(and)f Fn(E)p Fp(.)g(F)l(or)g(example,)h (pro)q(cedures)g(in)g Fn(B)f Fp(ma)o(y)g(in)o(v)o(ok)o(e)37 2198 y(exp)q(orted)e(pro)q(cedures)g(in)g Fn(D)g Fp(and)f Fn(E)p Fp(.)37 2318 y Fm(Subsystems)h(and)i(T)l(ub)q(es)p 37 2334 519 2 v 37 2404 a Fp(Using)f(subsystems,)e(designers)i(can)f (cluster)g(related)g(mo)q(dules,)h(as)e(sho)o(wn)g(in)i(the)f(second)g (diagram)f(of)37 2461 y(Figure)j(2,)g(where)f(mo)q(dules)i Fn(D)f Fp(and)f Fn(E)h Fp(are)f(group)q(ed)h(in)o(to)f(subsystem)h Fn(C)f Fp(and)g(mo)q(dule)i Fn(B)f Fp(is)g(group)q(ed)37 2517 y(in)o(to)g(subsystem)f Fn(A)p Fp(.)g(The)h(mo)q(dule)g(in)o (terconnections,)h(b)q(et)o(w)o(een)f(mo)q(dule)h Fn(B)e Fp(and)h(mo)q(dules)g Fn(D)g Fp(and)g Fn(E)p Fp(,)945 2640 y(4)p eop 5 4 bop 129 1145 a @beginspecial 35 @llx 184 @lly 576 @urx 607 @ury 3968 @rwi 2267 @rhi @setspecial % remember original state /origstate save def % build a temporary dictionary 20 dict begin % define space for color conversions /grays 1152 string def % space for gray scale line /npixls 0 def /rgbindx 0 def % lower left corner 35 184 translate % size of image (on paper, in 1/72inch coords) 541.44000 423.00000 scale % define 'colorimage' if it isn't defined % ('colortogray' and 'mergeprocs' come from xwd2ps % via xgrab) /colorimage where % do we know about 'colorimage'? { pop } % yes: pop off the 'dict' returned { % no: define one /colortogray { % define an RGB->I function /rgbdata exch store % call input 'rgbdata' rgbdata length 3 idiv /npixls exch store /rgbindx 0 store 0 1 npixls 1 sub { grays exch rgbdata rgbindx get 20 mul % Red rgbdata rgbindx 1 add get 32 mul % Green rgbdata rgbindx 2 add get 12 mul % Blue add add 64 idiv % I = .5G + .31R + .18B put /rgbindx rgbindx 3 add store } for grays 0 npixls getinterval } bind def % Utility procedure for colorimage operator. % This procedure takes two procedures off the % stack and merges them into a single procedure. /mergeprocs { % def dup length 3 -1 roll dup length dup 5 1 roll 3 -1 roll add array cvx dup 3 -1 roll 0 exch putinterval dup 4 2 roll putinterval } bind def /colorimage { % def pop pop % remove 'false 3' operands {colortogray} mergeprocs image } bind def } ifelse % end of 'false' case % define the colormap /cmap 21 string def % load up the colormap currentfile cmap readhexstring ffffff 000000 0000ff 00ff00 daa520 f2f2f2 e5e5e5 pop pop % lose return values from readhexstring % rlecmapimage expects to have 'w h bits matrix' on stack /rlecmapimage { /buffer 1 string def /rgbval 3 string def /block 384 string def % proc to read a block from file, and return RGB data { currentfile buffer readhexstring pop /bcount exch 0 get store bcount 128 ge { % it's a non-run block 0 1 bcount 128 sub { currentfile buffer readhexstring pop pop % look up value in color map /rgbval cmap buffer 0 get 3 mul 3 getinterval store % and put it in position i*3 in block block exch 3 mul rgbval putinterval } for block 0 bcount 127 sub 3 mul getinterval } { % else it's a run block currentfile buffer readhexstring pop pop % look up value in colormap /rgbval cmap buffer 0 get 3 mul 3 getinterval store 0 1 bcount { block exch 3 mul rgbval putinterval } for block 0 bcount 1 add 3 mul getinterval } ifelse } % end of proc false 3 colorimage } bind def 1152 900 8 % dimensions of data [1152 0 0 -900 0 900] % mapping matrix rlecmapimage 020181000101018100010101810001010181000101018100010101810001010181000101 018100010101810001010181000101018100010101810001010181000101018100010101 810001010181000101018100010101810001010181000101018100010101810001010181 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b(as)d(w)o(ell)i(as)e(the)h(tub)q(e)h(are)e(sho)o(wn)h(as)f(dotted)h (edges.)22 b(In)17 b(fact,)e(all)i(dotted)e(edges)h(are)37 2550 y(considered)h(tub)q(es)f(b)q(ecause)g(w)o(e)f(treat)f(mo)q(dule)j (in)o(terconnections)f(as)f(atomic)g(tub)q(es.)945 2640 y(6)p eop 7 6 bop 602 531 a @beginspecial 168 @llx 337 @lly 457 @urx 472 @ury 1700 @rwi @setspecial 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 2 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.86747 0 0 0.86747 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 109 -45 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 216 -112 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 7.00001 -130 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 7.00001 -83.0001 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 241 -78.0001 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 317 539 ] concat %I [ (S) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 198 490 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 198 437 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 462 495 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 434 456 ] concat %I [ (D) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 514 437 ] concat %I [ (E) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 99 -73.0001 ] concat %I 218 593 123 560 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 97 -76.0001 ] concat %I 121 555 121 515 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 99 -73.0001 ] concat %I 226 595 355 560 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 99 -73.0001 ] concat %I 355 560 330 528 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 101 -77.0001 ] concat %I 355 563 408 512 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 99 -73.0001 ] concat %I 123 558 348 558 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 101 -122 ] concat %I 123 558 323 572 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 105 -110 ] concat %I 115 542 399 542 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 297 -133 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 309 405 ] concat %I [ (Tube Graph) ] Text End End %I eop showpage end @endspecial 558 679 a Fp(Figure)16 b(4:)j Fm(Example)f(of)f(a)h(T)l (ub)q(e)g(Graph)108 816 y Fp(This)12 b(section)h(de\014ned)g(a)f(tub)q (e)g(graph)g(to)f(b)q(e)h(a)g(con)o(tainmen)o(t)g(tree)f(with)h(tub)q (es)h(b)q(et)o(w)o(een)f(its)g(v)o(ertices.)37 873 y(W)l(e)g(next)g (discuss)h(ho)o(w)e(tub)q(e)h(graphs)f(can)h(b)q(e)g(restricted)g(to)f (mak)o(e)g(them)h(useful)g(for)f(sp)q(ecifying)j(soft)o(w)o(are)37 929 y(structure.)37 1051 y Fh(3.1)56 b(Restricting)17 b(T)-5 b(ub)r(e)18 b(Edges)37 1137 y Fp(Criteria)k(for)e(automatic)h (comp)q(onen)o(t)g(clustering)i(include)g(pattern)e(matc)o(hing)g([15)o (,)g(2],)h(comp)q(onen)o(t)37 1193 y(coupling)16 b(and)e(cohesion)g (metrics)g([11)o(],)f(and)h(so)f(on.)19 b(Regardless)c(of)e(the)h (clustering)h(criteria,)f(the)g(result)37 1250 y(of)d(comp)q(onen)o(t)g (clustering)h(is)g(a)e(subsystem)h(decomp)q(osition)h(hierarc)o(h)o(y)l (.)19 b(Using)12 b(comp)q(onen)o(t)f(elision,)i(the)37 1306 y(in)o(ternals)g(of)e(subsystems)h(ma)o(y)f(either)i(b)q(e)f (hidden)h(or)f(exp)q(osed)g(dep)q(ending)i(on)e(the)g(kind)g(of)g (information)37 1362 y(the)k(soft)o(w)o(are)d(engineer)k(is)e(lo)q (oking)h(for.)108 1419 y(Similar)24 b(to)d(automatic)h(comp)q(onen)o(t) g(clustering,)j(the)d(criteria)h(for)e(automatic)h(in)o(terconnection) 37 1475 y(clustering)15 b(v)m(ary)l(.)k(In)14 b(our)f(approac)o(h,)g (the)g(in)o(terconnection)i(clustering)f(criteria)g(are)f(closely)h (tied)g(to)f(the)37 1532 y(restriction)g(of)e(tub)q(e)h(graphs)g(in)g (v)m(arious)g(w)o(a)o(ys.)18 b(More)11 b(sp)q(eci\014cally)l(,)k(tub)q (e)e(graphs)e(are)g(restricted)h(so)g(that)37 1588 y(in)o (terconnections)18 b(b)q(et)o(w)o(een)e(lo)o(w-lev)o(el)h(comp)q(onen)o (ts)f(\(mo)q(dules\))g(ma)o(y)g(o)q(ccur)g(only)g(when)h(p)q (ermissions)37 1645 y(\(tub)q(es\))f(b)q(et)o(w)o(een)f(higher-lev)o (el)j(comp)q(onen)o(ts)d(\(subsystems\),)f(exist.)108 1701 y(The)e(set)f(of)h(allo)o(w)o(ed)g(p)q(ermissions)h(is)f (determined)h(b)o(y)f(a)f(set)g(of)h(rules,)h(called)g Fn(wel)r(l-forme)n(dness)f(rules)p Fp(.)37 1821 y Fm(3.1.1)52 b(W)l(ell-F)l(ormed)18 b(T)l(ub)q(e)f(Graphs)37 1907 y Fp(W)l(e)f(will)h(consider)f(that)e(a)h(tub)q(e)h Fl(xT)6 b(y)17 b Fp(is)f(w)o(ell-formed)g(if)f(it)h(satis\014es)f(one)h(of)e (these)i(rules:)128 2001 y Fm(\(R1\))h Fp(Sibling)g(Rule:)k Fl(x)16 b Fp(and)f Fl(y)i Fp(are)e(prop)q(er)g(\()p Fl(x)p Fk(6)p Fp(=)p Fl(y)r Fp(\))g(siblings,)i(or)128 2057 y Fm(\(R2\))g Fp(P)o(aren)o(t-T)l(ub)q(e-Child)g(Rule:)k Fl(x)p Fp('s)15 b(paren)o(t)g(has)g(a)f(tub)q(e)i(to)f Fl(y)r Fp('s)f(paren)o(t,)h(or)128 2114 y Fm(\(R3\))i Fp(P)o(aren)o(t-T)l(ub)q(e)e(Rule:)21 b Fl(x)p Fp('s)15 b(paren)o(t)g(has)g(a)g(tub)q(e)h(to)e Fl(y)r Fp(,)h(or)128 2170 y Fm(\(R4\))i Fp(T)l(ub)q(e-Child)g(Rule:)22 b Fl(x)15 b Fp(has)g(a)g(tub)q(e)h(to)e Fl(y)r Fp('s)h(paren)o(t.)37 2264 y(Figure)h(5)f(giv)o(es)g(a)g(visual)h(represen)o(tation)g(of)e (the)i(set)f(of)f(allo)o(w)o(ed)i(tub)q(es.)k(The)c(lab)q(elled)i (edges)d(\()p Fl(C)j Fp(and)37 2320 y Fl(T)6 b Fp(\))15 b(represen)o(t)f(edges)h(in)g(a)g(tub)q(e)g(graph.)k(Eac)o(h)c(unlab)q (elled)i(dotted)e(edge)g(represen)o(ts)f(an)h(allo)o(w)o(ed)g(tub)q(e.) 37 2377 y(Note)j(that)f(the)h(sibling)i(v)o(ertices)e(for)f(rule)h (\(R1\))g(m)o(ust)f(b)q(e)h(distinct.)29 b(W)l(e)18 b(denote)g(the)g (set)f(of)h(allo)o(w)o(ed)37 2433 y(tub)q(es)i(of)e(a)g(tub)q(e)h (graph)f Fl(T)6 b(G)p Fp(=\()p Fl(V)j Fp(,)p Fl(C)s Fp(,)p Fl(T)d Fp(\))17 b(as)h Fl(T)874 2440 y Fg(A)902 2433 y Fp(\()p Fl(T)6 b(G)p Fp(\).)29 b(When)19 b(there)f(is)h(one)g (particular)g(tub)q(e)g(graph)37 2490 y Fl(T)6 b(G)16 b Fp(of)g(in)o(terest,)f(w)o(e)h(write)g Fl(T)563 2497 y Fg(A)607 2490 y Fp(instead)h(of)e Fl(T)844 2497 y Fg(A)872 2490 y Fp(\()p Fl(T)6 b(G)p Fp(\).)21 b(F)l(ollo)o(wing)c(is)f(the)g (formal)g(de\014nition)i(of)d(the)h(set)37 2546 y(of)f(allo)o(w)o(ed)h (tub)q(es:)945 2640 y(7)p eop 8 7 bop 248 506 a @beginspecial 79 @llx 483 @lly 537 @urx 582 @ury 3401 @rwi @setspecial 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.8 0 0 0.8 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 -153 -66 ] concat Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 300 113.726 ] concat %I 69 558 37 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 330 259 ] concat %I 39 512 3 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 357 206 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 331 110.726 ] concat %I 38 560 64 520 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 297 204 ] concat %I 39 512 3 3 Elli End End %I eop Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 190 692 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 234 691 ] concat %I [ (C) ] Text End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 13 267 ] concat %I 175 384 223 384 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 214 720 ] concat %I [ (p) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 180 647 ] concat %I [ (x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 241 647 ] concat %I [ (y) ] Text End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 337 192 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 267 46.726 ] concat %I 69 558 37 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 298 193 ] concat %I 39 512 3 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 364 140 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 338 38.726 ] concat %I 38 560 64 520 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 263 139 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.592992 0 0 1 238.077 321 ] concat %I 175 384 223 384 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.80625 0 0 1 -7.7101 268 ] concat %I 175 384 223 384 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 309 692 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 391 691 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 332 721 ] concat %I [ (p) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 375 719 ] concat %I [ (q) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 299 648 ] concat %I [ (x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 401 649 ] concat %I [ (y) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 352 720 ] concat %I [ (T) ] Text End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 503 193 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 409 46.726 ] concat %I 69 558 37 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 440 193 ] concat %I 39 512 3 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 405 139 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 309 322 ] concat %I 175 384 223 384 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 454 694 ] concat %I [ (C) ] Text End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 300 266 ] concat %I 147 384 240 437 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 474 720 ] concat %I [ (p) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 541 722 ] concat %I [ (y) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 439 648 ] concat %I [ (x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 499 720 ] concat %I [ (T) ] Text End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 598 195 ] concat %I 39 512 3 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 536 195 ] concat %I 39 512 3 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 625 143 ] concat %I 39 512 3 3 Elli End Begin %I Line %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.18182 599 41.726 ] concat %I 38 560 64 520 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 405 323 ] concat %I 175 384 223 384 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 651 694 ] concat %I [ (C) ] Text End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 402 299 ] concat %I 174 404 257 355 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 572 722 ] concat %I [ (x) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 634 723 ] concat %I [ (q) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-medium-r-*-100-* /Courier 10 SetF %I t [ 1 0 0 1 662 652 ] concat %I [ (y) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 600 722 ] concat %I [ (T) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 103 679 ] concat %I [ (T ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* /Times-Roman 12 SetF %I t [ 1 0 0 1 110 670 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -adobe-helvetica-medium-r-normal--34-240-100-100-p-176-iso8859-1 /helvetica 34 SetF %I t [ 1 0 0 1 133 690 ] concat %I [ (=) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -adobe-helvetica-medium-r-normal--34-240-100-100-p-176-iso8859-1 /helvetica 34 SetF %I t [ 1 0 0 1 263 693 ] concat %I [ (+) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -adobe-helvetica-medium-r-normal--34-240-100-100-p-176-iso8859-1 /helvetica 34 SetF %I t [ 1 0 0 1 410 696 ] concat %I [ (+) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -adobe-helvetica-medium-r-normal--34-240-100-100-p-176-iso8859-1 /helvetica 34 SetF %I t [ 1 0 0 1 549 688 ] concat %I [ (+) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 199 621 ] concat %I [ (\(R1\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 339 621 ] concat %I [ (\(R2\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 608 621 ] concat %I [ (\(R4\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 478 621 ] concat %I [ (\(R3\)) ] Text End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 28 108 ] concat %I 177 533 194 533 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 28 103 ] concat %I 177 533 194 533 Line End Begin %I Line %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 28 108 ] concat %I 192 540 179 522 Line End End %I eop showpage end @endspecial 325 654 a Fp(Figure)15 b(5:)20 b Fm(A)d(Visual)h(Represen) o(tation)g(of)f(Allo)o(w)o(ed)g(T)l(ub)q(es,)h Fl(T)1560 661 y Fg(A)39 778 y Fm(De\014nition)h(3:)h(Allo)o(w)o(ed)d(T)l(ub)q(es) 108 834 y Fp(Giv)o(en)f(a)f(tub)q(e)g(graph)g Fl(T)6 b(G)p Fp(=\()p Fl(V)s(;)i(C)q(;)g(T)d Fp(\),)12 b(its)j(set)g Fl(T)975 841 y Fg(A)1018 834 y Fp(of)g(allo)o(w)o(ed)h(tub)q(es)g(is:) 128 911 y Fl(T)155 918 y Fg(A)199 911 y Fk(\021)f(f)g Fp(\(x,y\))f Fk(j)h Fp(WFT)l(ub)q(e\(x,y\))f Fk(g)128 1024 y Fp(where)128 1137 y(WFT)l(ub)q(e\(x,y\))h Fk(\021)g(9)h Fp(p,q)f Fk(2)g Fl(V)25 b Fk(\017)15 b Fp(\(x)p Fk(6)p Fp(=y)g Fk(^)h Fp(p)p Fl(C)s Fp(x)f Fk(^)g Fp(p)p Fl(C)s Fp(y\))g Fk(_)106 b Fm(\(R1\))719 1194 y Fp(\(p)p Fl(C)s Fp(x)15 b Fk(^)h Fp(q)p Fl(C)s Fp(y)e Fk(^)i Fp(p)p Fl(T)6 b Fp(q\))15 b Fk(_)109 b Fm(\(R2\))719 1250 y Fp(\(p)p Fl(C)s Fp(x)15 b Fk(^)h Fp(p)p Fl(T)6 b Fp(y\))15 b Fk(_)253 b Fm(\(R3\))719 1307 y Fp(\(q)p Fl(C)s Fp(y)15 b Fk(^)g Fp(x)p Fl(T)6 b Fp(q\))301 b Fm(\(R4\))37 1384 y Fi(2)108 1440 y Fp(Note)16 b(that)f(the)h(righ)o(t)g(hand)g(side)h(of)f(the)g (de\014nition)i(of)d Fn(WFT)m(ub)n(e)g Fp(corresp)q(onds)i(to)e(the)h (graphs)g Fn(R1)37 1496 y Fp(to)f Fn(R4)h Fp(in)g(Figure)f(5.)39 1613 y Fm(De\014nition)k(4:)h(W)l(ell-F)l(ormed)d(T)l(ub)q(e)h(Graph) 108 1699 y Fp(A)e(tub)q(e)h(graph)f Fl(T)6 b(G)p Fp(=\()p Fl(V)k Fp(,)p Fl(C)s Fp(,)p Fl(T)c Fp(\))14 b(is)j(w)o(ell-formed)h(if) e(and)h(only)g(if)g(its)f(set)g(of)g(tub)q(es)h Fl(T)22 b Fp(is)17 b(a)f(subset)g(of)37 1756 y(its)g(set)f(of)g(allo)o(w)o(ed)g (tub)q(es)h Fl(T)535 1763 y Fg(A)563 1756 y Fp(:)108 1842 y Fl(W)6 b(F)g Fp(\()p Fl(T)g(G)p Fp(\))15 b Fk(\021)g Fl(T)22 b Fk(\022)15 b Fl(T)488 1849 y Fg(A)108 1929 y Fp(whic)o(h)h(can)f(b)q(e)h(rewritten)g(as:)128 2006 y Fl(W)6 b(F)g Fp(\()p Fl(T)g(G)p Fp(\))15 b Fk(\021)h(8)f Fp(\(x,y\))f Fk(2)i Fl(T)21 b Fk(\017)15 b Fp(WFT)l(ub)q(e\(x,y\))37 2083 y Fi(2)108 2139 y Fp(This)h(concludes)i(our)d(formal)h (de\014nition)h(of)f(tub)q(es)g(and)g(their)g(relationship)i(to)d (subsystem)g(hierar-)37 2196 y(c)o(hies.)21 b(In)14 b(the)g(follo)o (wing)g(section)g(w)o(e)g(presen)o(t)f(algorithms)h(that)f(are)g (useful)i(when)f(rev)o(erse)f(engineering)37 2252 y(soft)o(w)o(are)h (systems)h(using)h(subsystems)f(and)g(tub)q(es.)37 2392 y Fo(4)67 b(Algorithms)24 b(for)e(Clustering)h(Soft)n(w)n(are)f(In)n (terconnections)37 2494 y Fp(After)15 b(the)h(soft)o(w)o(are)d(comp)q (onen)o(ts)j(are)f(clustered)h(in)o(to)f(subsystems,)g(soft)o(w)o(are)e (engineers)k(can)e(use)h(the)37 2550 y(algorithms)h(presen)o(ted)f (next)g(to)g(cluster)h(the)f(in)o(terconnections)h(b)q(et)o(w)o(een)g (these)f(comp)q(onen)o(ts.)23 b(When)945 2640 y(8)p eop 9 8 bop 37 196 a Fp(soft)o(w)o(are)14 b(structures)i(are)f(mapp)q(ed)h (in)o(to)g(tub)q(e)g(graphs,)f(the)g(problem)i(of)e(clustering)i(in)o (terconnections)37 252 y(is)f(reduced)h(to)d(making)h(the)h(tub)q(e)g (graph)e(w)o(ell-formed.)108 309 y(Figure)19 b(6)e(sho)o(ws)h(an)g (example)h(of)f(ho)o(w)g(comp)q(osite)g(tub)q(e)h(in)o(terconnections)h (can)e(b)q(e)h(constructed)37 365 y(from)11 b(mo)q(dule)i(in)o (terconnections)g(and)f(a)f(subsystem)h(decomp)q(osition)h(hierarc)o(h) o(y)l(.)19 b(The)12 b(top)f(of)g(the)h(\014gure)37 421 y(sho)o(ws)i(an)h(in)o(terconnection)h(b)q(et)o(w)o(een)e(mo)q(dules)i Fn(D)f Fp(and)f Fn(E)p Fp(.)g(According)i(to)d(the)i(w)o (ell-formedness)h(rules,)37 478 y(the)e(corresp)q(onding)h(tub)q(e)f (graph)g(\(righ)o(t\))f(is)h(ill-formed)h(b)q(ecause)g(the)f(tub)q(e)g (from)f Fn(D)h Fp(to)f Fn(E)g Fp(is)i(ill-formed.)37 534 y(This)g(tub)q(e)g(can)g(b)q(e)g(made)f(w)o(ell-formed)h(b)o(y)g (adding)g(a)f(tub)q(e)h(from)e Fn(B)h Fp(to)g Fn(E)p Fp(,)g(as)g(sho)o(wn)g(in)h(the)f(middle)i(of)37 591 y(Figure)f(6.)20 b(Ho)o(w)o(ev)o(er,)13 b(the)h(corresp)q(onding)i(tub) q(e)f(graph)f(\(righ)o(t\))g(is)h(still)h(ill-formed)g(b)q(ecause)g (the)e(newly)37 647 y(added)19 b(tub)q(e)g(is)g(ill-formed.)31 b(This)19 b(tub)q(e)f(can)h(b)q(ecome)g(w)o(ell-formed)g(if)g(a)e(tub)q (e)i(b)q(et)o(w)o(een)g Fn(A)f Fp(and)g Fn(B)g Fp(is)37 704 y(added)e(\(b)q(ottom)f(of)g(Figure)g(6.)20 b(The)c(corresp)q (onding)g(tub)q(e)g(graph)f(is)h(no)o(w)f(w)o(ell-formed)h(b)q(ecause)g (all)g(of)37 760 y(its)g(tub)q(es)g(are)e(w)o(ell-formed.)108 817 y(By)g(making)f(the)h(tub)q(e)g(graph)f(w)o(ell-formed,)i(w)o(e)e (ha)o(v)o(e)g(also)h(succeeded)h(in)f(clustering)h(the)e(in)o(tercon-) 37 873 y(nections)18 b(of)f(the)g(corresp)q(onding)h(soft)o(w)o(are)d (structure.)25 b(The)18 b(b)q(ene\014ts)g(of)e(in)o(terconnection)j (clustering)37 930 y(are)j(not)e(apparen)o(t)h(from)g(examining)i (trivial)f(soft)o(w)o(are)d(structures)i(suc)o(h)h(as)f(the)g(one)h(in) g(Figure)g(6.)37 986 y(Ho)o(w)o(ev)o(er,)14 b(the)i(b)q(ene\014ts)g(b)q (ecome)g(more)e(ob)o(vious)i(in)g(larger)f(systems)g(suc)o(h)g(as)g (Lin)o(ux)h(\(Figure)f(3\).)108 1042 y(When)h(sp)q(ecifying)h(the)e (complexit)o(y)h(of)f(our)g(algorithms)g(w)o(e)g(will)i(use)e(the)h (follo)o(wing)f(de\014nitions:)106 1131 y Fk(\017)22 b(j)p Fp(V)p Fk(j)15 b Fp(is)g(the)h(n)o(um)o(b)q(er)f(of)g(v)o (ertices)g(in)h(the)g(tub)q(e)g(graph,)106 1219 y Fk(\017)22 b(j)p Fp(T)p Fk(j)14 b Fp(is)i(the)f(n)o(um)o(b)q(er)h(of)f(tub)q(es)g (in)h(the)g(tub)q(e)f(graph,)106 1307 y Fk(\017)22 b Fl(heig)r(ht)15 b Fp(is)h(the)f(heigh)o(t)h(of)f(the)g(tub)q(e)h(graph) f(con)o(tainmen)o(t)g(tree,)f Fk(j)p Fp(V)p Fk(j)h Fp(in)h(the)f(w)o (orst)f(case.)37 1395 y(The)j(w)o(orst)d(case)i(complexit)o(y)g(of)g (eac)o(h)g(of)f(the)h(follo)o(wing)g(algorithms)g(dep)q(ends)h(on)f (the)g(complexit)o(y)g(of)37 1452 y(the)f(primitiv)o(e)h(op)q (erations.)528 1435 y Fj(1)567 1452 y Fp(It)e(has)h(b)q(een)g(sho)o(wn) f(elsewhere)i([8)o(],)e(that)f(the)i(w)o(orst)e(case)h(complexit)o(y)h (of)37 1508 y(all)i(primitiv)o(e)f(op)q(erations)g(is)f(constan)o(t)g (O\(1\).)39 1614 y Fm(Algorithm)j(1:)i(In)o(v)m(alid)e(T)l(ub)q(e)37 1660 y Fp(Bo)q(olean)24 b(function)g Fn(invalidT)m(ub)n(e)d Fp(c)o(hec)o(ks)i(if)g(an)g(ill-formed)h(tub)q(e)f(cannot)g(b)q(ecome)g (w)o(ell-formed)h(b)o(y)37 1705 y(adding)18 b(other)e(tub)q(es)h(to)f (the)g(graph.)24 b(This)17 b(situation)f(o)q(ccurs)h(when)g(the)g(tub)q (e)g(is)g(a)f(lo)q(op)h(or)f(the)g(tub)q(e)37 1751 y(v)o(ertices)k(are) e(prop)q(er)i(ancestors)e(or)g(descenden)o(ts)j(of)d(eac)o(h)h(other.) 31 b(\(Recall)20 b(that)f(w)o(ell-formed)g(tub)q(es)37 1797 y(m)o(ust)j(satisfy)g(rules)h Fn(R1-R4)p Fp(.\))41 b(In)o(v)m(alid)24 b(tub)q(es)e(m)o(ust)g(ev)o(en)o(tually)h(b)q(e)g (deleted)g(in)g(order)f(to)f(ac)o(hiev)o(e)37 1842 y(w)o (ell-formedness.)h(The)15 b(complexit)o(y)h(of)f Fn(invalidT)m(ub)n(e)e Fp(is)j(O\(1\).)114 1910 y Ff(function)f(in)o(v)n(alidT)m(ub)q(e\(x,y)h (:)h Fe(V)9 b Ff(\))j(:)17 b(b)q(o)q(olean)191 1956 y(result)d(x=y)f Fd(_)g Ff(isAncestor\(x,y\))h Fd(_)e Ff(isAncestor\(y)m(,x\))114 2002 y(end)i(in)o(v)n(alidT)m(ub)q(e)37 2021 y Fi(2)39 2127 y Fm(Algorithm)k(2:)i(W)l(ell-F)l(ormed)d(T)l(ub)q(e)37 2172 y Fp(Bo)q(olean)j(function)f Fn(WFT)m(ub)n(e)e Fp(c)o(hec)o(ks)i (if)g(a)f(tub)q(e)h(is)g(w)o(ell-formed.)30 b(That)18 b(is,)h(the)g(tub)q(e)g(satis\014es)f(rules)37 2218 y Fn(R1-R4)j Fp(from)e(Section)i(3.1.1.)31 b(Note,)21 b(that)e(w)o(e)g (used)h(the)g(notation)f Fn(p)n(ar\(x\))h Fp(to)f(mean)g(the)h(paren)o (t)f(of)37 2264 y(v)o(ertex)c Fn(x)p Fp(.)20 b(The)c(complexit)o(y)g (of)e Fn(WFT)m(ub)n(e)h Fp(is)g(O\(1\).)114 2332 y Ff(function)g(WFT)m (ub)q(e\(x,y)e(:)k Fe(V)9 b Ff(\))k(:)k(b)q(o)q(olean)191 2377 y(result)d Fd(:)e Ff(\(isRo)q(ot\(x\))j Fd(_)d Ff(isRo)q (ot\(y\)\))j Fd(^)345 2423 y Ff(\(\(x)p Fd(6)p Ff(=y)e Fd(^)f Ff(par\(x\)=par\(y\)\))i Fd(_)e Ff(tub)q(e\(par\(x\),par\(y\)\)) j Fd(_)d Ff(tub)q(e\(par\(x\),y\))i Fd(_)f Ff(tub)q(e\(x,par\(y\)\)\)) 114 2469 y(end)h(WFT)m(ub)q(e)p 37 2507 735 2 v 89 2534 a Fc(1)107 2550 y Ff(These)f(trivial)i(algorithms,)g(suc)o(h)e(as)h Fb(isA)o(nc)n(esto)o(r\(x,y)o(\))c Ff(and)k Fb(isR)n(o)n(ot\(x\))c Ff(are)j(not)g(describ)q(ed)i(in)f(this)g(pap)q(er.)945 2640 y Fp(9)p eop 10 9 bop 37 2045 a @beginspecial 18 @llx 240 @lly 598 @urx 698 @ury 4535 @rwi @setspecial 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 4 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.8 0 0 0.8 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 -15.1808 ] concat Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.13095 12.7471 -182.456 ] concat %I 31 480 161 560 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 13.3374 -102.795 ] concat %I 71 500 121 530 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1.00813 0 0 1.16667 260.674 -198.925 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 105.337 416.205 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 47.6627 447.543 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 408.747 449.374 ] concat %I [ (C) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 256.904 -102.144 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 346.904 416.856 ] concat %I [ (E) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 13.5784 -104.747 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 102.494 416.422 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.681042 0 0 0.791639 43.9596 0.0508728 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 70.6507 438.747 ] concat %I [ (B) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 -16.7096 -311.433 ] concat %I 171 428 171 439 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.538462 0 0 0.5 137.829 224.603 ] concat %I 3 314 356 314 338 351 360 3 MLine End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.551282 0 0 0.471591 132.74 234.818 ] concat %I 3 314 394 314 415 351 394 3 MLine End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.75 0 0 3.7886 45.2603 -1228.21 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.75 0 0 1.53592 163.031 -253.838 ] concat %I 171 428 171 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.776241 0 0 1 43.2158 -6.89133 ] concat %I 165 440 291 440 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.551282 0 0 0.471591 94.3665 247.409 ] concat %I 3 315 395 315 416 356 393 3 MLine End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.776241 0 0 1 40.6255 -48.5178 ] concat %I 172 440 291 440 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.538462 0 0 0.5 98.3713 214.422 ] concat %I 3 315 356 315 339 359 358 3 MLine End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.75 0 0 3.51799 163.031 -1113.51 ] concat %I 172 428 172 439 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.28257 0 0 1 -66.5576 -38.4817 ] concat %I 172 440 290 440 Line End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.813376 0 0 0.703636 47.3401 116.133 ] concat %I 4 110 422 172 422 300 422 337 422 4 MLine End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.26231 0 0 1 -62.4287 -19.4817 ] concat %I 172 440 291 440 Line End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 3.13155 0 0 1.96458 -70.4758 -623.372 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 29.8917 337.265 ] concat %I [ (S) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 0 -7.5903 ] concat Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.13095 15.3495 14.2426 ] concat %I 31 480 161 560 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 15.9399 93.9035 ] concat %I 71 500 121 530 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1.00813 0 0 1.16667 263.277 -2.2262 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 107.94 612.904 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 50.2652 644.242 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 411.35 646.073 ] concat %I [ (C) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 259.506 94.5546 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 349.507 613.555 ] concat %I [ (E) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 16.1809 91.9522 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 106.181 610.952 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.681042 0 0 0.791639 47.6464 194.581 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 73.2531 635.447 ] concat %I [ (B) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.28927 0 0 1 -64.9854 177.217 ] concat %I 172 440 291 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.30052 0 0 1 -66.4822 158.217 ] concat %I 172 440 290 440 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg White 1 1 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1.66757 -13.5649 -115.276 ] concat %I 171 428 171 439 Line End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.5 154.073 420.76 ] concat %I 3 314 356 314 338 351 360 3 MLine End Begin %I MLine %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.5 0 0 0.471591 153.531 430.433 ] concat %I 3 314 394 314 415 351 394 3 MLine End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.801756 0 0 0.86 50.1057 246.394 ] concat %I 4 110 422 172 422 300 422 337 422 4 MLine End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 3.13155 0 0 1.96458 -69.8131 -426.444 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 29.4701 532.025 ] concat %I [ (S) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t u Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.13095 12.5302 207.688 ] concat %I 31 480 161 560 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 13.1205 287.349 ] concat %I 71 500 121 530 Rect End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1.00813 0 0 1.16667 260.457 191.219 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 105.12 806.349 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 47.4459 837.687 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 408.53 839.518 ] concat %I [ (C) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 261.024 285.831 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 351.024 804.831 ] concat %I [ (E) ] Text End Begin %I MLine %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 0.887742 0 0 0.86 29.9546 439.839 ] concat %I 4 110 422 172 422 300 422 337 422 4 MLine End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Blue 0 0 1 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 13.3615 285.398 ] concat %I 71 500 121 530 Rect End Begin %I Text %I cfg White 1 1 1 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 103.361 804.398 ] concat %I [ (D) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 0.681042 0 0 0.791639 44.827 388.026 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 70.4338 828.892 ] concat %I [ (B) ] Text End Begin %I Rect %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 3.13155 0 0 1.96458 -69.1505 -230.601 ] concat %I 31 480 161 560 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* /Helvetica-Bold 14 SetF %I t [ 1 0 0 1 32.0603 730.88 ] concat %I [ (S) ] Text End End %I eop Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 377.916 282.47 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 275.916 197.47 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 275.916 244.47 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 509.916 249.47 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 585.916 866.47 ] concat %I [ (S) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 466.916 817.47 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 469.084 770.976 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 730.916 822.47 ] concat %I [ (C) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 367.916 254.47 ] concat %I 218 593 123 560 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 365.916 251.47 ] concat %I 121 555 121 515 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 367.916 254.47 ] concat %I 226 595 355 560 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 380.422 202.289 ] concat %I 109 512 336 555 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 509.53 196.638 ] concat %I 212 566 4 3 Elli End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 366.578 204.422 ] concat %I 121 555 121 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 275.494 149.337 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 469.747 721.759 ] concat %I [ (D) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 600.795 258.638 ] concat %I 121 555 120 508 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 731.578 774.337 ] concat %I [ (E) ] Text End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 380.747 84.6989 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 278.747 -0.301178 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 278.747 46.6987 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 512.747 51.6987 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 588.747 668.699 ] concat %I [ (S) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 469.747 619.699 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 471.916 573.205 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 733.747 624.699 ] concat %I [ (C) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 370.747 56.6987 ] concat %I 218 593 123 560 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 368.747 53.6987 ] concat %I 121 555 121 515 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 370.747 56.6987 ] concat %I 226 595 355 560 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 372.747 8.78317 ] concat %I 123 558 344 557 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 383.253 4.51816 ] concat %I 109 512 336 555 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 512.361 -1.13254 ] concat %I 212 566 4 3 Elli End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 369.41 6.65057 ] concat %I 121 555 121 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 278.325 -48.4337 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 472.578 523.988 ] concat %I [ (D) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 603.626 60.8674 ] concat %I 121 555 120 508 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 734.41 576.566 ] concat %I [ (E) ] Text End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 379.241 -116.325 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 277.241 -201.325 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 277.241 -154.325 ] concat %I 212 566 4 3 Elli End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 511.241 -149.325 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 587.241 467.675 ] concat %I [ (S) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 468.241 418.675 ] concat %I [ (A) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 470.41 372.181 ] concat %I [ (B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 732.241 423.675 ] concat %I [ (C) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 369.241 -144.325 ] concat %I 218 593 123 560 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 367.241 -147.325 ] concat %I 121 555 121 515 Line End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 369.241 -144.325 ] concat %I 226 595 355 560 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 369.241 -144.325 ] concat %I 123 558 348 558 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 371.241 -192.241 ] concat %I 123 558 344 557 Line End Begin %I Line %I b 13107 3 0 1 [2 2 2 2 2 2 2 2] 15 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 381.747 -196.506 ] concat %I 109 512 336 555 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 510.855 -202.157 ] concat %I 212 566 4 3 Elli End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 367.904 -194.374 ] concat %I 121 555 121 515 Line End Begin %I Elli %I b 65535 2 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 276.819 -249.458 ] concat %I 212 566 4 3 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 471.072 322.964 ] concat %I [ (D) ] Text End Begin %I Line %I b 65535 3 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 602.12 -140.157 ] concat %I 121 555 120 508 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-bold-r-*-140-* /Times-Bold 14 SetF %I t [ 1 0 0 1 732.904 375.542 ] concat %I [ (E) ] Text End End %I eop showpage end @endspecial 534 2193 a Fp(Figure)15 b(6:)20 b Fm(Example)e(of)f(T)l (ub)q(e)h(Clustering)934 2640 y Fp(10)p eop 11 10 bop 37 196 a Fi(2)39 301 y Fm(Algorithm)18 b(3:)i(W)l(ell-F)l (ormed)d(T)l(ub)q(e)h(Graph)37 347 y Fp(Bo)q(olean)i(function)g Fn(isWFT)m(ub)n(eGr)n(aph)e Fp(c)o(hec)o(ks)i(the)f(w)o(ell-formedness) h(of)e(a)h(tub)q(e)h(graph)f(ro)q(oted)f(at)h Fl(r)q Fp(.)37 393 y(Starting)e(from)e Fl(r)q Fp(,)h(it)h(visits)g(eac)o(h)f 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b(w)o(ork)g(suggests) f(sev)o(eral)h(opp)q(ortunities)h(for)f(further)g(researc)o(h,)g (namely)h(the)f(dev)o(elopmen)o(t)37 1512 y(of)d(op)q(erations)h(for)e (manipulating)j(tub)q(e)f(graphs)f(represen)o(ting)h(soft)o(w)o(are)d (structures.)29 b(Manipulation)37 1569 y(op)q(erations)14 b(on)g(soft)o(w)o(are)e(structures)h(include)j(the)e(addition)h(and)f (remo)o(v)m(al)g(of)f(mo)q(dules)i(or)e(subsystems)37 1625 y(\(addition)k(and)f(remo)o(v)m(al)f(of)h(a)f(tub)q(e)h(graph)f(v) o(ertices)h(or)f(subtrees\),)h(the)f(replacemen)o(t)i(of)e(a)g (subsystem)37 1682 y(with)g(another)f(subsystem)g(\(replacemen)o(t)g (of)g(tub)q(e)h(graph)f(subtrees\),)f(the)i(iden)o(ti\014cation)h(and)e (remo)o(v)m(al)37 1738 y(unnecessary)19 b(tub)q(es,)f(and)f(so)g(on.)27 b(Also)18 b(of)f(in)o(terest)g(is)h(the)g(e\013ect)f(of)g(these)g(op)q (erations)h(on)f(the)h(w)o(ell-)37 1794 y(formedness)h(of)f(tub)q(e)h (graphs.)29 b(F)l(or)18 b(example,)h(do)g(these)f(op)q(erations)h (preserv)o(e)f(the)h(w)o(ell-formedness)37 1851 y(of)f(tub)q(e)h (graphs?)30 b(If)18 b(not,)g(should)h(these)g(op)q(erations)f(also)g (add)h(new)f(tub)q(es)h(in)g(order)f(to)g(mak)o(e)f(tub)q(e)37 1907 y(graphs)e(w)o(ell-formed?)22 b(Finally)l(,)16 b(the)f (computational)g(complexit)o(y)h(of)f(these)g(op)q(erations)g(is)h(of)e (in)o(terest.)108 1964 y(Related)j(researc)o(h)e(is)h(curren)o(tly)g(b) q(eing)g(conducted)h(to)e(iden)o(tify)h(di\013eren)o(t)g(kinds)g(of)f (tub)q(es,)h(as)f(w)o(ell)37 2020 y(as)20 b(other)g(kinds)h(of)e(w)o (ell-formedness)j(rules.)35 b(These)20 b(ideas)h(will)h(enable)f(soft)o (w)o(are)d(designers)j(to)f(use)37 2077 y(soft)o(w)o(are)12 b(structures,)i(suc)o(h)f(as)h(those)f(describ)q(ed)j(in)e(this)g(pap)q (er,)g(as)f(a)g(means)h(of)f(con)o(trolling)i(the)e(scop)q(e)37 2133 y(of)i(soft)o(w)o(are)f(comp)q(onen)o(ts)h([9)o(].)934 2640 y(13)p eop 14 13 bop 37 196 a Fo(References)57 278 y Ff([1])22 b Fa(Biggerst)n(aff,)16 b(T.)h(J.)22 b Ff(Design)17 b(Reco)o(v)o(ery)e (for)g(Main)o(tenance)i(and)e(Reuse.)23 b Fb(IEEE)16 b(Computer)e(22)p Ff(,)g(7)h(\(July)h(1989\),)120 324 y(36{49.)57 386 y([2])22 b Fa(Carmichael,)g(I.,)g(Tzerpos,)g(V.,)g(and) e(Hol)n(t,)i(R.)e(C.)35 b Ff(Design)20 b(Main)o(tenance:)31 b(Unexp)q(ected)20 b(Arc)o(hitectural)120 432 y(In)o(teractions)10 b(\(Exp)q(erience)h(Rep)q(ort\).)g(In)e Fb(Pr)n(o)n(c)n(e)n(e)n(dings)e (of)i(the)g(Internationa)o(l)e(Confer)n(enc)n(e)h(on)h(Softwar)n(e)f (Maintenanc)n(e)120 478 y Ff(\(1995\),)13 b(pp.)g(134{137.)57 540 y([3])22 b Fa(Chik)o(ofsky,)16 b(E.)f(J.,)h(and)f(Cr)o(oss,)i(J.)f (H.)21 b Ff(Rev)o(erse)15 b(Engineering)i(and)e(Design)h(Reco)o(v)o (ery:)21 b(A)14 b(T)m(axonom)o(y.)21 b Fb(IEEE)120 586 y(Softwar)n(e)12 b(7)p Ff(,)g(1)h(\(Jan)o(uary)h(1990\),)f(13{17.)57 648 y([4])22 b Fa(Dean,)13 b(T.)i(R.)h Fb(Softwar)n(e)c(Char)n (acterization)e(Using)i(Conne)n(ctivity)o Ff(.)i(PhD)f(thesis,)h (Departmen)o(t)f(of)g(Computing)h(and)120 693 y(Information)g(Science,) g(Queen's)g(Univ)o(ersit)o(y,)g(1993.)57 756 y([5])22 b Fa(DeRemer,)12 b(F.,)g(and)g(Kr)o(on,)h(H.)f(H.)i Ff (Programming{in{the{La)q(rge)g(V)m(ersus)c(Programming{in)q({the{S)q (mall)q(.)16 b Fb(IEEE)120 801 y(T)m(r)n(ansactions)11 b(on)i(Softwar)n(e)f(Engine)n(ering)f(2)p Ff(,)h(2)h(\(June)g(1976\),)g (80{86.)57 864 y([6])22 b Fa(Garlan,)16 b(D.)k Ff(First)15 b(In)o(ternational)h(W)m(orkshop)g(on)e(Arc)o(hitectures)i(for)e(Soft)o (w)o(are)g(Systems)h(W)m(orkshop)g(Summary.)120 909 y Fb(Softwar)n(e)d(Engine)n(ering)f(Notes)h(20)p Ff(,)g(3)h(\(July)g (1995\),)g(84{89.)57 972 y([7])22 b Fa(Garlan,)13 b(D.,)g(Tichy,)h(W.,) f(and)h(P)m(a)o(ulisch,)f(F.)i Ff(Summary)d(of)g(the)g(Dagstuhl)i(W)m (orkshop)f(on)g(Soft)o(w)o(are)e(Arc)o(hitec-)120 1017 y(ture.)17 b Fb(Softwar)n(e)12 b(Engine)n(ering)f(Notes)h(20)p Ff(,)g(3)h(\(July)g(1995\),)h(63{83.)57 1079 y([8])22 b Fa(Hol)n(t,)d(R.)f(C.,)i(and)e(Mancoridis,)j(S.)29 b Ff(Using)18 b(T)m(ub)q(e)f(Graphs)h(to)f(Mo)q(del)h(Arc)o(hitectural) h(Designs)g(of)e(Soft)o(w)o(are)120 1125 y(Systems.)28 b(T)m(ec)o(h.)16 b(Rep.)h(CSRI-308,)g(Computer)g(Science)h(Researc)o(h) f(Institute,)i(Univ)o(ersit)o(y)f(of)e(T)m(oron)o(to,)h(Octob)q(er)120 1171 y(1994.)57 1233 y([9])22 b Fa(Mancoridis,)17 b(S.)j Fb(Contr)n(ol)r(ling)13 b(the)g(Inter)n(actions)f(of)i(A)o(r)n(chite)n (ctur)n(al)e(Design)h(Comp)n(onents)f(Using)h(Sc)n(oping)g(R)o(ules)p Ff(.)120 1279 y(PhD)h(thesis,)f(Departmen)o(t)h(of)f(Computer)g (Science,)i(Univ)o(ersit)o(y)f(of)f(T)m(oron)o(to,)g(1996.)37 1341 y([10])23 b Fa(Mancoridis,)d(S.,)e(and)g(Hol)n(t,)g(R.)g(C.)27 b Ff(Extending)19 b(Programming)f(En)o(vironmen)o(ts)h(to)d(Supp)q(ort) i(Arc)o(hitectural)120 1387 y(Design.)h(In)13 b Fb(Pr)n(o)n(c)n(e)n(e)n (dings)e(of)j(the)e(Seventh)g(Internationa)o(l)f(IEEE)j(Workshop)e(on)h (Computer-A)o(ide)n(d)e(Softwar)n(e)h(Engi-)120 1432 y(ne)n(ering)i Ff(\(July)g(1995\),)f(pp.)g(110{119.)37 1495 y([11])23 b Fa(M)158 1492 y(\177)157 1495 y(uller,)14 b(H.)g(A.,)g(and)f(Klashinsky,)h(K.)j Ff(Rigi:)h(A)12 b(System)h(for)f(Programming-in-the-Large.)19 b(In)12 b Fb(Pr)n(o)n(c)n(e)n(e)n(dings)f(of)120 1540 y(the)i(10th)f(IEEE)h (International)d(Confer)n(enc)n(e)i(on)h(Softwar)n(e)f(Engine)n(ering)h Ff(\(Singap)q(ore,)i(1988\),)e(pp.)g(11{15.)37 1603 y([12])23 b Fa(Murphy,)17 b(G.,)f(Notkin,)h(D.,)f(and)h(Sulliv)m(an,)f(K.)24 b Ff(Soft)o(w)o(are)15 b(Re\015exion)i(Mo)q(dels:)22 b(Bridging)c(the)d(Gap)g(b)q(et)o(w)o(een)120 1648 y(Source)j(and)g (High-Lev)o(el)h(Mo)q(dels.)31 b(In)17 b Fb(Pr)n(o)n(c)n(e)n(e)n(dings) e(of)i(the)g(A)o(CM)h(SIGSOFT)f(Symp)n(osium)f(on)h(F)m(oundation)o(s)e (of)120 1694 y(Softwar)n(e)d(Engine)n(ering)f(\(FSE'95\))h Ff(\(W)m(ashington,)j(D.C.,)d(Octob)q(er)h(1995\),)h(pp.)f(18{28.)37 1756 y([13])23 b Fa(Perr)n(y,)12 b(D.)g(E.)i Ff(Soft)o(w)o(are)c(In)o (terconnection)k(Mo)q(dels.)h(In)c Fb(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)i (the)g(9th)g(IEEE)g(International)d(Confer)n(enc)n(e)120 1802 y(on)13 b(Softwar)n(e)f(Engine)n(ering)h Ff(\(Mon)o(terey)m(,)h (California,)g(1987\),)g(pp.)f(61{69.)37 1864 y([14])23 b Fa(Prieto-Diaz,)15 b(R.,)f(and)g(Neighbors,)h(J.)g(M.)j Ff(Mo)q(dule)d(In)o(terconnection)g(Languages.)k Fb(The)14 b(Journal)e(of)i(Systems)120 1910 y(and)e(Softwar)n(e)h(6)k Ff(\(1986\),)c(307{334.)37 1972 y([15])23 b Fa(Schw)m(anke,)14 b(R.)g(W.,)h(Al)n(tucher,)h(R.)e(Z.,)h(and)g(Pla)n(toff,)e(M.)i(A.)k Ff(Disco)o(v)o(ering,)d(Visualizin)q(g,)g(and)e(Con)o(trolling)120 2018 y(Soft)o(w)o(are)j(Structure.)29 b(In)17 b Fb(Pr)n(o)n(c)n(e)n(e)n (dings)d(of)j(the)f(Fifth)g(Internationa)o(l)e(Workshop)i(on)g(Softwar) n(e)g(Sp)n(e)n(ci\014c)n(atio)o(n)e(and)120 2063 y(Design)g Ff(\(Pittsburgh,)g(P)o(ennsylv)n(ani)q(a,)h(Ma)o(y)f(1989\),)f(pp.)g (147{150.)37 2126 y([16])23 b Fa(W)l(a)n(ters,)15 b(R.)g(C.,)h(and)g (Chik)o(ofsky,)f(E.)g(J.)21 b Ff(Sp)q(ecial)16 b(Issue)e(on)h(Rev)o (erse)g(Engineering.)23 b Fb(Communic)n(ations)12 b(of)i(the)120 2171 y(A)o(CM)g(37)p Ff(,)e(5)h(\(Ma)o(y)g(1994\),)g(23{93.)934 2640 y Fp(14)p eop end userdict /end-hook known{end-hook}if