Forests, frames, and games: Algorithms for matroid sums and applications (original) (raw)

References

  1. M. Aigner,Combinatorial Theory, Springer-Verlag, New York, 1979.
    MATH Google Scholar
  2. J. Bruno, Matroids, Graphs and Resistance Networks, Ph.D. Dissertation, Dept. Electrical Engineering, City College of New York, New York, 1967.
    Google Scholar
  3. J. Bruno and L. Weinberg, A constructive graph-theoretic solution of the Shannon switching game,IEEE Trans. Circuit Theory,17(1), 1970, 74–81.
    MathSciNet Google Scholar
  4. J. Bruno and L. Weinberg, The principal minors of a matroid,Linear Algebra Appl.,4, 1971, 17–54.
    Article MATH MathSciNet Google Scholar
  5. N. Chiba and T. Nishizeki, Arboricity and subgraph listing algorithms,SIAM J. Comput.,14(1), 1985, 210–223.
    Article MATH MathSciNet Google Scholar
  6. E. A. Dinic, Algorithm for solution of a problem of maximum flow in a network with power estimation,Soviet Math. Dokl.,11(5), 1970, 1277–1280.
    Google Scholar
  7. J. Edmonds, Minimum partition of a matroid into independent subsets,J. Res. Nat. Bur. Standards,69B, 1965, 67–72.
    MathSciNet Google Scholar
  8. J. Edmonds, Lehman's switching game and a theorem of Tutte and Nash-Williams,J. Res. Nat. Bur. Standards,69B, 1965, 73–77.
    MathSciNet Google Scholar
  9. S. Even and R. E. Tarjan, Network flow and testing graph connectivity,SIAM J. Comput.,4(4), 1975, 507–518.
    Article MATH MathSciNet Google Scholar
  10. G. N. Frederickson, Data structures for on-line updating of minimum spanning trees, with applications,SIAM J. Comput.,14(4), 1985, 781–798.
    Article MATH MathSciNet Google Scholar
  11. H. N. Gabow and M. Stallmann, Efficient algorithms for graphic matroid intersection and parity,Automata, Languages and Programming: 12th Colloquium, Lecture Notes in Computer Science, Vol. 194, W. Brauer, ed., Springer-Verlag, Berlin, 1985, pp. 210–220.
    Google Scholar
  12. H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union,J. Comput. System Sci.,30(2), 1985, 209–221.
    Article MATH MathSciNet Google Scholar
  13. H. N. Gabow and R. E. Tarjan, A linear-time algorithm for finding a minimum spanning pseudoforest,Inform. Process. Lett.,27(5), 1988, 259–263.
    Article MATH MathSciNet Google Scholar
  14. H. N. Gabow and R. E. Tarjan, Algorithms for two bottleneck optimization problems,J. Algorithms,9(3), 1988, 411–417.
    Article MATH MathSciNet Google Scholar
  15. H. N. Gabow and R. E. Tarjan, Almost-optimum speed-ups of algorithms for bipartite matching and related problems,Proc. 20th Annual ACM Symp. on Theory of Computing, 1988, pp. 514–527.
  16. G. Gallo, M. D. Grigoriadis, and R. E. Tarjan, A fast parametric maximum flow algorithm and applications,SIAM J. Comput.,18(1), 1989, 30–55.
    Article MATH MathSciNet Google Scholar
  17. D. Gusfield, Connectivity and edge-disjoint spanning trees,Inform. Process. Lett.,16, 1983, 87–89.
    Article MATH MathSciNet Google Scholar
  18. J. Hopcroft and R. Karp, An_n_ 5/2 algorithm for maximum matchings in bipartite graphs,SIAM J. Comput.,2(4), 1973, 225–231.
    Article MATH MathSciNet Google Scholar
  19. H. Imai, Network-flow algorithms for lower-truncated transversal polymatroids,J. Oper. Res. Soc. Japan,26(3), 1983, 186–210.
    MATH MathSciNet Google Scholar
  20. M. Iri and S. Fujishige, Use of matroid theory in operations research, circuits and systems theory,Internat. J. Systems Sci.,12(1), 1981, 27–54.
    Article MATH MathSciNet Google Scholar
  21. A. Itai and M. Rodeh, The multi-tree approach to reliability in distributed networks,Inform. and Control,79, 1988. 43–59.
    MATH MathSciNet Google Scholar
  22. G. Kishi and Y. Kajitani, Maximally distant trees and principal partition of a linear graph,IEEE Trans. Circuit Theory,16(3), 1969, 323–330.
    MathSciNet Google Scholar
  23. G. Laman, On graphs and rigidity of plane skeletal structures,J. Engrg. Math.,4(4), 1970, 331–340.
    Article MATH MathSciNet Google Scholar
  24. E. L. Lawler,Combinatorial Optimization: Networks and Matroids, Holt, Rhinehart, and Winston, New York, 1976.
    MATH Google Scholar
  25. A. Lehman, A solution to the Shannon switching game,J. Soc. Indust. Appl. Math.,12, 1964, 687–725.
    Article MATH MathSciNet Google Scholar
  26. L. Lovász and Y. Yemini, On generic rigidity in the plane,SIAM J. Algebraic Discrete Methods,3, 1982, 91–98.
    Article MATH MathSciNet Google Scholar
  27. L. R. Matthews, Bicircular matroids,Quart. J. Math. Oxford,28(2), 1977, 213–228.
    Article MATH MathSciNet Google Scholar
  28. C. St. J. A. Nash-Williams, Edge-disjoint spanning trees of finite graphs,J. London Math. Soc.,36, 1961, 445–450.
    Article MATH MathSciNet Google Scholar
  29. T. Ohtsuki, Y. Ishizaki, and H. Watanabe, Topological degrees of freedom and mixed analysis of electrical networks,IEEE Trans. Circuit Theory,17(4), 1970, 491–499.
    Article MathSciNet Google Scholar
  30. J.-C. Picard and M. Queyranne, A network flow solution to some nonlinear 0-1 programming problems, with applications to graph theory,Networks,12, 1982, 141–159.
    Article MATH MathSciNet Google Scholar
  31. A. Recski,Matroid Theory and Its Applications in Electric Network Theory and in Statics, Springer-Verlag, New York, 1989.
    Google Scholar
  32. J. Roskind and R. E. Tarjan, A note on finding minimum-cost edge-disjoint spanning trees,Math. Oper. Res.,10(4), 1985, 701–708.
    MATH MathSciNet Google Scholar
  33. B. Servatuis, Birigidity in the plane,SIAM J. Discrete Math.,2(4), 1989, 582–589.
    Article MathSciNet Google Scholar
  34. D. D. Sleator and R. E. Tarjan, A data structure for dynamic trees,J. Comput. System Sci.,26, 1983, 362–391.
    Article MATH MathSciNet Google Scholar
  35. R. E. Tarjan,Data Structures and Network Algorithms, SIAM Monograph, Philadelphia, PA, 1983.
  36. T.-S. Tay, Rigidity of multi-graphs. I. Linking rigid bodies in_n_-space,J. Combin. Theory Ser. B,36, 1984, 95–112.
    Article MATH MathSciNet Google Scholar
  37. W. T. Tutte, On the problem of decomposing a graph into connected factors,J. London Math. Soc.,36, 1961, 221–230.
    Article MATH MathSciNet Google Scholar
  38. D. J. A. Welsh,Matroid Theory, Academic Press, New York, 1976.
    MATH Google Scholar
  39. H. H. Westermann, Efficient Algorithms for Matroid Sums, Ph.D. Dissertation, Dept. Computer Science, University of Colorado at Boulder, Boulder, CO, 1987.
    Google Scholar
  40. N. White and W. Whiteley, The algebraic geometry of motions of bar-and-body frameworks,SIAM J. Algebraic Discrete Methods,8(1), 1987, 1–32.
    Article MATH MathSciNet Google Scholar
  41. W. Whiteley, The union of matroids and the rigidity of frameworks,SIAM J. Discrete Math.,1(2), 1988, 237–255.
    Article MATH MathSciNet Google Scholar

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