Approximation metatheorems for classes with bounded expansion

TL;DR

This paper develops approximation algorithms for monotone maximization problems expressible in first-order logic across various graph classes, including bounded expansion and those with sublinear separators, extending previous results significantly.

Contribution

It introduces new approximation metatheorems applicable to broader graph classes, providing constant-factor, QPTAS, and PTAS algorithms, as well as exact subexponential algorithms.

Findings

Constant-factor approximation in bounded expansion graphs

QPTAS in classes with strongly sublinear separators

PTAS in fractionally treewidth-fragile classes

Abstract

We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in any class of graphs with bounded expansion, * a QPTAS in any class with strongly sublinear separators, and * a PTAS in any fractionally treewidth-fragile class (which includes all common classes with strongly sublinear separators. Moreover, our tools also give an exact subexponential-time algorithm in any class with strongly sublinear separators.