Showing papers by "Wing-Kin Sung published in 1997"

All-Cavity Maximum Matchings

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 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

General techniques for comparing unrooted evolutionary trees

Abstract: This paper presents two sets of techniques for comparing unrooted evolutionary trees, namely, label compression and four-way dvnamic programming. The technique of four-way dynamic programming transforms existing algorithms for computing rooted maximum agree ment subtrees into new ones for unrooted trees. Let n be the size of the two input trees. This technique leads to an O(n log n)-time algorithm for unrooted trees whose degrees are bounded by a constant, matching the best known complexity for the rooted binary case. The technique of label compression is not based on dynamic programming. With this technique, we obtain an O(nl”5 log n)-time algorithm for unrooted trees with arbitrary degrees, also matching the best algorithm for the rooted unbounded degree case.