Properties of nowhere dense graph classes related to independent set problem

TL;DR

This paper introduces fixed-parameter algorithms for the r-independent set problem in nowhere dense graph classes, providing efficient solutions with runtime bounds dependent on parameters k and r.

Contribution

It presents new fixed-parameter algorithms for the r-independent set problem applicable to nowhere dense and more general graph classes.

Findings

Algorithms run in time f(k, r)*G for nowhere dense classes.

Alternative algorithms work on broader graph classes.

Provides theoretical bounds for problem complexity.

Abstract

A set is called r-independent, if every two vertices of it are in distance greater then r. In the r-independent set problem with parameter k, we ask whether in a given graph G there exists an r-independent set of size k. In this work we present an algorithm for this problem, which applied to a graph from any fixed nowhere dense class, works in time bounded by f(k, r)*G, for some function f. We also present alternative algorithm, with running time bounded by g(k, r)*G, working on slightly more general classes of graphs.