Towards constant-factor approximation for chordal / distance-hereditary vertex deletion

Jungho Ahn; Eun Jung Kim; Euiwoong Lee

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arXiv · 2009.00809

Towards constant-factor approximation for chordal / distance-hereditary vertex deletion

Jungho Ahn·Eun Jung Kim·Euiwoong Lee

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Abstract

For a family of graphs $\mathcal{F}$, Weighted $\mathcal{F}$-Deletion is the problem for which the input is a vertex weighted graph $G=(V,E)$ and the goal is to delete $S\subseteq V$ with minimum weight such that $G\setminus S\in\mathcal{F}$. Designing a constant-factor approximation algorithm for large subclasses of perfect graphs has been an interesting research direction. Block graphs, 3-leaf power graphs, and interval graphs are known to admit constant-factor approximation algorithms, but the question is open for chordal graphs and distance-hereditary graphs. In this paper, we add one more class to this list by presenting a constant-factor approximation algorithm when $F$ is the intersection of chordal graphs and distance-hereditary graphs. They are known as ptolemaic graphs and form a superset of both block graphs and 3-leaf power graphs above. Our proof presents new properties and algorithmic results on inter-clique digraphs as well as an approximation algorithm for a variant of Feedback Vertex Set that exploits this relationship (named Feedback Vertex Set with Precedence Constraints), each of which may be of independent interest.

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BibTeX RIS

Jungho Ahn, Eun Jung Kim, Euiwoong Lee. 2020-09-02. Towards constant-factor approximation for chordal / distance-hereditary vertex deletion. https://arxiv.org/abs/2009.00809

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