An Experimental Study of Algorithms for Online Bipartite Matching

TL;DR

This study evaluates various algorithms for online bipartite matching on practical instances, revealing that simple greedy algorithms often perform comparably to complex worst-case optimized algorithms in real-world scenarios.

Contribution

It demonstrates that greedy algorithms are highly competitive with complex algorithms for practical online bipartite matching, challenging the emphasis on worst-case performance.

Findings

Greedy algorithms perform as well as complex algorithms on practical data.

Non-greedy versions of algorithms perform worse than greedy ones.

Greediness is the most crucial property for effective online bipartite matching.

Abstract

We perform an experimental study of algorithms for online bipartite matching under the known i.i.d. input model with integral types. In the last decade, there has been substantial effort in designing complex algorithms with the goal of improving worst-case approximation ratios. Our goal is to determine how these algorithms perform on more practical instances rather than worst-case instances. In particular, we are interested in whether the ranking of the algorithms by their worst-case performance is consistent with the ranking of the algorithms by their average-case/practical performance. We are also interested in whether preprocessing times and implementation difficulties that are introduced by these algorithms are justified in practice. To that end we evaluate these algorithms on different random inputs as well as real-life instances obtained from publicly available repositories. We compare these algorithms against several simple greedy-style algorithms. Most of the complex algorithms in the literature are presented as being non-greedy (i.e., an algorithm can intentionally skip matching a node that has available neighbors) to simplify the analysis. Every such algorithm can be turned into a greedy one without hurting its worst-case performance. On our benchmarks, non-greedy versions of these algorithms perform much worse than their greedy versions. Greedy versions perform about as well as the simplest greedy algorithm by itself. This, together with our other findings, suggests that simplest greedy algorithms are competitive with the state-of-the-art worst-case algorithms for online bipartite matching on many average-case and practical input families. Greediness is by far the most important property of online algorithms for bipartite matching.