DIVIDE-AND-CONQUER APPROXIMATION ALGORITHM FOR VERTEX COVER.

The vertex cover problem is a classical NP–complete problem for which the best worstcase approximation ratio is 2–o(1). In this paper, we use a collection of simple graph transformations, each of which guarantees an approximation ratio of 3 2 , to find approximate vertex covers for a large collection of randomly generated graphs and test graphs from various sources. The graph reductions are extremely fast, and even though they by themselves are not guaranteed to find a vertex cover, we manage to find a 3 2 –approximate vertex cover for almost every single graph in our collection. The few graphs that we cannot solve have specific structure: they are triangle–free, with a minimum degree of at least 3, a lower bound of n 2 on the optimal vertex cover, and are unlikely to have a large bipartite subgraph. [ABSTRACT FROM AUTHOR]