Fully-dynamic Weighted Matching Approximation in Practice

TL;DR

This paper presents practical implementations of algorithms for dynamic weighted matching, demonstrating that a random walk-based approach outperforms previous methods in efficiency and quality on various dynamic graph instances.

Contribution

First implementation of non-trivial dynamic weighted matching algorithms using random walks and dynamic programming, and adaptation of Stubbs and Williams' approach with empirical evaluation.

Findings

Random walk algorithm outperforms Stubbs/Williams in time/quality tradeoff

Results often close to optimal weighted matchings

Empirical study on extensive dynamic graph instances

Abstract

Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is based on random walks/paths combined with dynamic programming. The second algorithm has been introduced by Stubbs and Williams without an implementation. Roughly speaking, their algorithm uses dynamic unweighted matching algorithms as a subroutine (within a multilevel approach); this allows us to use previous work on dynamic unweighted matching algorithms as a black box in order to obtain a fully-dynamic weighted matching algorithm. We empirically study the algorithms on an extensive set of dynamic instances and compare them with optimal weighted matchings. Our experiments show that the random walk algorithm typically fares much better than Stubbs/Williams (regarding the time/quality tradeoff), and its results are often not far from the optimum.