The maximum weight perfect matching problem for complete weighted graphs is in PC

  • Authors:

  • Osiakwan; Akl

  • Affiliations:

  • Dept. of Comput. & Inf. Sci., Queen's Univ., Kingston, Ont., Canada;Dept. of Comput. & Inf. Sci., Queen's Univ., Kingston, Ont., Canada

  • Venue:
  • SPDP '90 Proceedings of the 1990 IEEE Second Symposium on Parallel and Distributed Processing
  • Year:
  • 1990

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Abstract

There are efficient sequential algorithms that use linear programming (LP) for computing maximum weight matchings. 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. The authors present an LP-based parallel algorithm for maximum weight matching in a complete weighted graph. The algorithm is designed for the EREW PRAM model of parallel computation, and runs in O(n/sup 3//p+n/sup 2/logn) time for p