Random Walk in Large Real-World Graphs for Finding Smaller Vertex Cover

The problem of finding a minimum vertex cover (MinVC) in a graph is a prominent NP-hard problem of great importance in both theory and application. During recent decades, there has been much interest in finding optimal or near-optimal solutions to this problem. Many existing heuristic algorithms for MinVC are based on local search strategies. Recently, an algorithm called FastVC takes a first step towards solving the MinVC problem for large real-world graphs. However, FastVC may be trapped by local minima during the local search stage due to the lack of suitable diversification mechanisms. In this work, we design a new random walk strategy to help FastVC escape from local minima. Experiments conducted on a broad range of large real-world graphs show that our algorithm outperforms state-of-the-art algorithms on most classes of the benchmark and finds smaller vertex covers on a considerable portion of the graphs.