Abstract
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 G u denote the graph formed by deleting u from G. The all-cavity maximum matching problem asks for a maximum weight matching in G u 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(n 21og n + nm). Our algorithms are based on novel linear-time reductions among problems of computing shortest paths and all-cavity maximum matchings.
Research supported in part by NSF Grants CCR-9531028.
Research supported in part by RGC (The Research Grants Council of Hong Kong) Grants 338/065/0027 and 338/065/0028.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kao, MY., Lam, T.W., Sung, W.K., Ting, H.F. (1997). All-cavity maximum matchings. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_39
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DOI: https://doi.org/10.1007/3-540-63890-3_39
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