# The time complexity of maximum matching by simulated annealing

@article{Sasaki1988TheTC, title={The time complexity of maximum matching by simulated annealing}, author={Galen H. Sasaki and Bruce E. Hajek}, journal={J. ACM}, year={1988}, volume={35}, pages={387-403} }

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…

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