Balance between complexity and quality: local search for minimum vertex cover in massive graphs

Abstract

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard problem with important applications. There has been much interest in developing heuristic algorithms for finding a good vertex cover in graphs. In practice, most heuristic algorithms for MinVC are based on the local search method. Previously, local search algorithms for MinVC have focused on solving academic benchmarks where the graphs are of relatively small size, and they are not suitable for solving massive graphs as they usually have highcomplexity heuristics. In this paper, we propose a simple and fast local search algorithm called FastVC for solving MinVC in massive graphs, which is based on two low-complexity heuristics. Experimental results on a broad range of real world massive graphs show that FastVC finds much better vertex covers (and thus also independent sets) than state of the art local search algorithms for MinVC.