Implementation and Comparison of Heuristics for the Vertex Cover Problem on Huge Graphs

摘要

We present in this paper an experimental study of six heuristics for a well-studied NP-complete graph problem: the vertex cover. These algorithms are adapted to process huge graphs. Indeed, executed on a current laptop computer, they offer reasonable CPU running times (between twenty seconds and eight hours) on graphs for which sizes are between 200 • 10~6 and 100 • 10~9 vertices and edges. We have run algorithms on specific graph families (we propose generators) and also on random power law graphs. Some of these heuristics can produce good solutions. We give here a comparison and an analysis of results obtained on several instances, in terms of quality of solutions and complexity, including running times.