Approximation metatheorems for classes with bounded expansion
Discrete Mathematics
2021-10-12 v3 Combinatorics
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.
Cite
@article{arxiv.2103.08698,
title = {Approximation metatheorems for classes with bounded expansion},
author = {Zdeněk Dvořák},
journal= {arXiv preprint arXiv:2103.08698},
year = {2021}
}
Comments
35 pages, no figures; revised the presentation