Combinatorial approximation of maximum $k$-vertex cover in bipartite graphs within ratio~0.7

TL;DR

This paper introduces a new purely combinatorial algorithm for the maximum k-vertex cover problem in bipartite graphs, achieving a better approximation ratio of 0.7 compared to previous algorithms.

Contribution

It presents the first combinatorial algorithm that surpasses the 2/3 approximation ratio for this problem.

Findings

Achieves approximation ratio of 0.7

Improves over previous greedy and simple algorithms

Provides a new combinatorial approach

Abstract

We propose a \textit{purely combinatorial algorithm} for \mkvc{} in bipartite graphs, achieving approximation ratio~0.7. The only combinatorial algorithms currently known until now for this problem are the natural greedy algorithm, that achieves ratio 0.632, and an easy~$2/3$-approximation algorithm presented in \cite{DBLP:journals/corr/BonnetEPS14}.