Section: New Results

Approximation algorithms for maximum matchings in undirected graphs

We propose heuristics for approximating the maximum cardinality matching on undirected graphs. Our heuristics are based on the theoretical body of a certain type of random graphs, and are made practical for real-life ones. The idea is based on judiciously selecting a subgraph of a given graph and obtaining a maximum cardinality matching on this subgraph. We show that the heuristics have an approximation guarantee of around $0.866-log\left(n\right)/n$ for a graph with $n$ vertices. Experiments for verifying the theoretical results in practice are provided. The findings are published in a conference proceedings [25].