Distributed algorithms for covering, packing and maximum weighted matching

TL;DR

This paper develops distributed algorithms with poly-logarithmic rounds for covering, packing, and maximum weighted matching problems, achieving approximation ratios comparable to centralized algorithms.

Contribution

It introduces new distributed algorithms for submodular covering, fractional packing, and weighted matching, matching centralized approximation ratios in a parallel setting.

Findings

Poly-logarithmic-round distributed algorithms for submodular covering.

Distributed D-approximation algorithms for fractional packing and weighted matching.

Parallel 2-approximation algorithms for specific covering problems.

Abstract

This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of variables in any constraint. Special cases include Covering Mixed Integer Linear Programs (CMIP), and Weighted Vertex Cover (with D=2). Via duality, the paper also gives poly-logarithmic-round, distributed D-approximation algorithms for Fractional Packing linear programs (where D is the maximum number of constraints in which any variable occurs), and for Max Weighted c-Matching in hypergraphs (where D is the maximum size of any of the hyperedges; for graphs D=2). The paper also gives parallel (RNC) 2-approximation algorithms for CMIP with two variables per constraint and Weighted Vertex Cover. The algorithms are randomized. All of the approximation ratios exactly match those of comparable centralized algorithms.