Constructing a Perfect Matching is in Random NC

摘要

This document shows 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. (Author)