A More Reliable Greedy Heuristic for Maximum Matchings in Sparse Random Graphs

TL;DR

This paper introduces a new greedy algorithm for maximum matchings in sparse random graphs, demonstrating high reliability across various degrees, unlike existing heuristics that fail at certain densities.

Contribution

The paper presents a novel greedy heuristic that consistently finds maximum matchings in sparse random graphs regardless of the expected degree c.

Findings

The new algorithm reliably finds maximum matchings in random graphs with constant expected degree c.

Experimental results show the algorithm outperforms traditional greedy heuristics.

The approach is effective across a wide range of graph densities.

Abstract

We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c>0, independent of the value of c. This is contrary to the behavior of commonly used greedy matching heuristics which are known to have some range of c where they probably fail to compute a maximum matching.