Fixed-Treewidth-Efficient Algorithms for Edge-Deletion to Intersection Graph Classes

TL;DR

This paper develops faster fixed-parameter tractable algorithms for edge-deletion problems to transform graphs into permutation and interval graph classes, improving upon generic Courcelle's theorem-based approaches.

Contribution

The paper provides explicit, efficient FPT algorithms for edge-deletion to permutation and interval graphs, surpassing the speed of Courcelle's theorem-based methods.

Findings

Algorithms are significantly faster than Courcelle's theorem-based solutions.

Explicit algorithms are developed for permutation and interval graph classes.

The methods improve practical efficiency of edge-deletion problems.

Abstract

For a graph class $\mathcal{C}$, the $\mathcal{C}$-Edge-Deletion problem asks for a given graph $G$ to delete the minimum number of edges from $G$ in order to obtain a graph in $\mathcal{C}$. We study the $\mathcal{C}$-Edge-Deletion problem for $\mathcal{C}$ the permutation graphs, interval graphs, and other related graph classes. It follows from Courcelle's Theorem that these problems are fixed parameter tractable when parameterized by treewidth. In this paper, we present concrete FPT algorithms for these problems. By giving explicit algorithms and analyzing these in detail, we obtain algorithms that are significantly faster than the algorithms obtained by using Courcelle's theorem.