Approximation schemes for bounded distance problems on fractionally treewidth-fragile graphs

TL;DR

This paper develops polynomial-time approximation schemes for distance-based maximization problems on graphs with fractional treewidth fragility, expanding efficient solutions to broader graph classes with sublinear separators.

Contribution

It introduces approximation schemes for distance problems on fractionally treewidth-fragile graphs, a significant generalization beyond bounded treewidth graphs.

Findings

Polynomial-time approximation schemes for these problems.

Extension to all classes with sublinear separators.

Applicable to many natural graph classes.

Abstract

We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally treewidth-fragile graph classes, a property that is true for many natural graph classes with sublinear separators. We also provide quasipolynomial-time approximation schemes for these problems in all classes with sublinear separators.