A 0.821-ratio purely combinatorial algorithm for maximum $k$-vertex   cover in bipartite graphs
  Our goal in this paper is to propose a \textit{combinatorial algorithm} that beats the only such algorithm known previously, the greedy one. We study the polynomial approximation of the Maximum Vertex Cover Problem in bipartite graphs by a purely combinatorial algorithm and present a computer assisted analysis of it, that finds the worst case approximation guarantee that is bounded below by~0.821. 
Edouard Bonnet, Bruno Escoffier, Vangelis Paschos, Georgios Stamoulis
cs.DS