Massively Parallel Algorithms for b-Matching

Abstract

This paper presents an O(log log đ) round massively parallel algorithm for 1 + ε approximation of maximum weighted b-matchings, using near-linear memory per machine. Here đ denotes the average degree in the graph and ε is an arbitrarily small positive constant. Recall that b-matching is the natural and well-studied generalization of the matching problem where different vertices are allowed to have different numbers of incident edges in the matching.