All-cavity maximum matchings

  • Ming-Yang Kao
  • Tak Wah Lam
  • Wing Kin Sung
  • Hing Fung Ting
Session 8A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)


Let G = (X, Y, E) be a bipartite graph with integer weights on the edges. Let n, m, and N denote the vertex count, the edge count, and an upper bound on the absolute values of edge weights of G, respectively. For a vertex u in G, let Gu denote the graph formed by deleting u from G. The all-cavity maximum matching problem asks for a maximum weight matching in Gu for all u in G. This problem finds applications in optimal tree algorithms for computational biology. We show that the problem is solvable in O(√nmlog(nN)) time, matching the currently best time complexity for merely computing a single maximum weight matching in G. We also give an algorithm for a generalization of the problem where both a vertex from X and one from Y can be deleted. The running time is O(n21og n + nm). Our algorithms are based on novel linear-time reductions among problems of computing shortest paths and all-cavity maximum matchings.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ming-Yang Kao
    • 1
  • Tak Wah Lam
    • 2
  • Wing Kin Sung
    • 2
  • Hing Fung Ting
    • 2
  1. 1.Department of Computer ScienceYale UniversityNew Haven
  2. 2.Department of Computer ScienceUniversity of Hong KongHong Kong

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