New approximation algorithms for the vertex cover problem

Abstract

The vertex cover is a classical NP-complete problem that has received great attention these last decades. A conjecture states that there is no c-approximation polynomial algorithm for it with c a constant strictly less than 2. In this paper we propose a new algorithm with approximation ratio strictly less than 2 (but non constant). Moreover we show that our algorithm has the potential to return any optimal solution. © 2013 Springer-Verlag.