A las vegas rnc algorithm for maximum matching

Abstract

Recently two randomized algorithms were discovered that find a maximum matching in an arbitrary graph in polylog time, when run on a parallel random access machine. Both are Monte Carlo algorithms — they have the drawback that with non-zero probability the output is a non-maximum matching. We use the min-max formula for the size of a maximum matching to convert any Monte Carlo maximum matching algorithm into a Las Vegas (error-free) one. The resulting algorithm returns (with high probability) a maximum matching and a certificate proving that the matching is indeed maximum.

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Research supported by DARPA grant N00039-84-C-0098 and by a US Army Research Office fellowship.

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Karloff, H.J. A las vegas rnc algorithm for maximum matching. Combinatorica 6, 387–391 (1986). https://doi.org/10.1007/BF02579264

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AMS subject classification (1986)

  • 05 C 99
  • 68 E 10