Simple Distributed Weighted Matchings

TL;DR

This paper presents a simple and efficient distributed algorithm for weighted matching that improves the approximation factor to 2, surpassing previous complex methods and achieving the best known results.

Contribution

It introduces a straightforward distributed implementation of a greedy weighted matching algorithm with a 2-approximation factor, improving upon prior complex algorithms.

Findings

Distributed greedy algorithm achieves a 2-approximation

Simplifies previous complex algorithms

Provides the best known approximation ratio for distributed weighted matching

Abstract

Wattenhofer [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yields the best known distributed approximation algorithm for this problem so far.