CONSTRUCTING A PERFECT MATCHING IS IN RANDOM NC.

Abstract

It is shown that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i. e. , the problem is solvable in polylog time by a randomized parallel algorithm using a polynomial-bounded number of processors. It is also shown that several related problems lie in Random NC. These include: constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; constructing a maximum-cardinality matching; constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; and constructing a maximum s - t flow in a directed graph whose edge weights are given in unary.