Splitting $B_2$-VPG graphs into outer-string and co-comparability graphs

TL;DR

This paper demonstrates that $B_2$-VPG graphs can be decomposed into simpler graph classes, enabling improved approximation algorithms for key problems like independent set and clique cover.

Contribution

It introduces a method to decompose $B_2$-VPG graphs into outer-string and permutation graphs, enhancing algorithmic approaches for these graphs.

Findings

Decomposition into $O(\log n)$ outer-string graphs.

Decomposition into $O(\log^3 n)$ permutation graphs.

Improved approximation algorithms for hereditary graph problems.

Abstract

In this paper, we show that any $B_2$-VPG graph (i.e., an intersection graph of orthogonal curves with at most 2 bends) can be decomposed into $O(\log n)$ outerstring graphs or $O(\log^3 n)$ permutation graphs. This leads to better approximation algorithms for hereditary graph problems, such as independent set, clique and clique cover, on $B_2$-VPG graphs.