Constructing compact rectiliner planar layouts using canonical representation of planar graphs (original) (raw)

We present a new linear-time algorithm to construct a rectilinear planar layout (horvertrepresentation. visibility representation) for a given planar graph. Our approach is based on the canonical representation of planar graphs and it is basically different from previous algorithms. If we direct the edges from lower-numbered vertices to higher-numbered vertices and there are)I vertices out of which k vertices have out-degree greater than in-degree, then the maximum width of the constructed layout is r/ 1 max jt/~",(1.,)-d,"(f.,).O1 <2/t-46(1\-2)62n-4. and the maximum height is /I+ I <n. where It is length of the longest directed path. We discuss the selection of a good canonical numbering to be used when constructing layouts. We also show how our algorithm can be applied to compute planar layouts for planar graphs using other drawings for vertices than horizontal segments. In these layouts the drawings for vertices may have arbitrary nonequal sizes and shapes. We know of two earlier linear-time methods for constructing rectilinear planar layouts. First, in 1978 Otten and van Wijk [9] proposed an algorithm for constructing