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We propose a new greedy algorithm for the maximum cardinality matchingproblem. We give experimental evidence that this algorithm is likely to find amaximum matching in random graphs with constant expected degree c>0,independent of the value of c. This is contrary to the behavior of commonlyused greedy matching heuristics which are known to have some range of c wherethey probably fail to compute a maximum matching.

A More Reliable Greedy Heuristic for Maximum Matchings in Sparse Random Graphs