Abstract
We give a class of heuristic algorithms for minimum weight perfect matching on a complete edge- weighted graph K.V/ satisfying the triangle inequality, where V is a set of an even number, n, of vertices. This class is a generalization of the Onethird heuristics, the hypergreedy heuristic, and it possibly employs any given exact or approximate perfect matching algorithm as an auxiliary heuristic to an appropriate subgraph of K.V/. In particular, by using the heuristic of Gabow et al. (3) as its auxiliary heuristic, our algorithm can obtain a solution whose weight is at most. 3 log3 log3 log3 nC 2/ times the weight of the optimal solution in O.n 2 log log log n/ time, or a solution with an error of 3.log3 log3 n/ 0:125 i 1i n O. n 2 /time.
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