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• W2026317193 abstract "A matching M of a graph G = (V,E) is a subset of the set of edges E such that no two edges in M are adjacent. A maximum weight (perfect) matching of a (complete) weighted graph is a (perfect) matching of the graph where the sum of the weights of the edges in the matching is maximum. There are efficient sequential algorithms that use linear programming (LP) for computing maximum weight matchings. These are primal-dual algorithms. A number of randomized parallel algorithms for maximum weight matchings have also appeared in the literature. Finding a deterministic parallel algorithm for computing maximum weight matchings in complete graphs has been an open problem for some time. Since LP is known to be P-complete, then, by the parallel computation thesis, it is unlikely that there exists an NC algorithm that uses LP to solve the maximum weight matching problem. In this paper, we present an LP-based parallel algorithm for maximum weight perfect matching in a complete weighted graph. The algorithm is designed for the EREW PRAM model of parallel computation, and runs in O(n3/p + n2 logn) time for p ≤n, where p is the number of processors and n is the number of vertices in the graph. This algorithm provides an optimal speedup with respect to the O(n3) sequential LP-based solution of Gabow [18] or Lawler [28], for p≤n/logn. This shows that the maximum weight perfect matching problem for complete graphs is in the class of problems (known as PC∗) for which an optimal speedup parallel algorithm can be designed on the PRAM using a polynomial number of processors. This is the first deterministic optimal speedup parallel algorithm designed for the maximum weight matching problem on complete graphs." @default.
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• W2026317193 date "1995-01-01" @default.
• W2026317193 modified "2023-10-18" @default.
• W2026317193 title "THE MAXIMUM WEIGHT PERFECT MATCHING PROBLEM FOR COMPLETE WEIGHTED GRAPHS IS IN PC∗†" @default.
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• W2026317193 doi "https://doi.org/10.1080/10637199508915506" @default.
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