The time complexity of maximum matching by simulated annealing

  • Authors:
  • Galen H. Sasaki;Bruce Hajek

  • Affiliations:
  • Coordinated Science Laboratory, Urbana, IL;Coordinated Science Laboratory, Urbana, IL

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1988

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Abstract

The random, heuristic search algorithm called simulated annealing is considered for the problem of finding the maximum cardinality matching in a graph. It is shown that neither a basic form of the algorithm, nor any other algorithm in a fairly large related class of algorithms, can find maximum cardinality matchings such that the average time required grows as a polynomial in the number of nodes of the graph. In contrast, it is also shown for arbitrary graphs that a degenerate form of the basic annealing algorithm (obtained by letting “temperature” be a suitably chosen constant) produces matchings with nearly maximum cardinality in polynomial average time.