Simple PTAS's for families of graphs excluding a minor

TL;DR

This paper presents simple local search algorithms that serve as polynomial-time approximation schemes for key graph problems on graphs excluding a fixed minor, expanding the toolkit for efficiently approximating solutions in such graph classes.

Contribution

It introduces straightforward local search algorithms that act as PTAS for Maximum Independent Set, Minimum Vertex Cover, and Minimum Dominating Set on minor-free graphs, a novel approach in this context.

Findings

Algorithms are polynomial-time approximation schemes.

Effective for graphs with a fixed forbidden minor.

Applicable to multiple classical graph problems.

Abstract

We show that very simple algorithms based on local search are polynomial-time approximation schemes for Maximum Independent Set, Minimum Vertex Cover and Minimum Dominating Set, when the input graphs have a fixed forbidden minor.