Exploiting Reduction Rules and Data Structures: Local Search for Minimum Vertex Cover in Massive Graphs

TL;DR

This paper introduces a local search algorithm for the NP-hard Minimum Vertex Cover problem on massive graphs, leveraging reduction rules and data structures to improve solution quality over existing methods.

Contribution

It presents a novel local search algorithm that exploits reduction rules and data structures, achieving better results on real-world massive graphs compared to prior algorithms.

Findings

The algorithm outperforms state-of-the-art local search methods.

It provides new insights into the complexities of common heuristics.

Experimental results demonstrate improved solution quality.

Abstract

The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal or near-optimal solutions. In this paper we propose a local search algorithm that exploits reduction rules and data structures to solve the MinVC problem in such graphs. Experimental results on a wide range of real-word massive graphs show that our algorithm finds better covers than state-of-the-art local search algorithms for MinVC. Also we present interesting results about the complexities of some well-known heuristics.