Approximability of the Vertex Cover Problem in Power Law Graphs

TL;DR

This paper presents an approximation algorithm for the Minimum Vertex Cover Problem in Power Law Graphs, achieving a ratio of 2 minus a positive function of beta, improving understanding of algorithmic performance on such networks.

Contribution

It introduces a novel deterministic rounding procedure combined with existing methods to improve approximation ratios specifically for Power Law Graphs.

Findings

Expected approximation ratio of 2 - f(beta) for Min-VC in PLGs.

New rounding technique achieves 3/2 ratio on low degree vertices.

Enhanced understanding of Min-VC approximability in power law networks.

Abstract

In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) for random Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al., where f(beta) is a strictly positive function of the parameter beta. We obtain this result by combining the Nemhauser and Trotter approach for Min-VC with a new deterministic rounding procedure which achieves an approximation ratio of 3/2 on a subset of low degree vertices for which the expected contribution to the cost of the associated linear program is sufficiently large.