Complete Algorithms on Minimum Vertex-Cover

The vertex cover problem is a classical NP-complete problem for which the best worst-case approximation ratio is 2-o(1). This paper analyzes the hierarchical Bayesian optimization algorithm (hBOA) on minimum vertex cover for standard classes of random graphs. The performance of hBOA is compared with that of the branch-and-bound problem solver (BB), the simple genetic algorithm(GA) and the parallel simulated annealing (PSA). The results indicate that BB is significantly outperformed by all the other methods, which is expected as BB is a complete search algorithm and minimum vertex cover is an NP-complete problem. The best performance is achieved with hBOA; nonetheless, the performance differences between hBOA and other evolutionary algorithms are relatively small, indicating that mutation-based search and recombination-based search lead to similar performance on problem instances.