Abstract
The problem of computing a matching of maximum weight in a given edge-weighted graph is not known to be P -hard or in RNC . This paper presents two parallel approximation algorithms for this problem. The first is an RNC -approximation scheme, i.e., an RNC algorithm that computes a matching of weight at least 1−ε times the maximum for any fixed constant ε>0. The other is an NC approximation algorithm achieving an approximation ratio of 1/(2+ε) for any fixed constant ε>0.
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