A 0.821-ratio purely combinatorial algorithm for maximum $k$-vertex cover in bipartite graphs

TL;DR

This paper introduces a new purely combinatorial algorithm for the maximum k-vertex cover problem in bipartite graphs, achieving a worst-case approximation ratio of at least 0.821, surpassing previous greedy algorithms.

Contribution

It presents a novel combinatorial algorithm with a computer-assisted analysis that improves the approximation guarantee for maximum k-vertex cover in bipartite graphs.

Findings

Achieves a 0.821 approximation ratio in the worst case.

Outperforms previous greedy algorithms.

Provides a computer-assisted proof of the approximation guarantee.

Abstract

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.