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Towards Constant-Factor Approximation for Chordal / Distance-Hereditary Vertex Deletion

Authors Jungho Ahn , Eun Jung Kim , Euiwoong Lee

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Author Details

Jungho Ahn
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
Eun Jung Kim
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France
Euiwoong Lee
  • Department of Computer Science, New York University, NY, USA

Funding

Jungho Ahn: the Institute for Basic Science (IBS-R029-C1). Eun Jung Kim: ANR JCJC project "ASSK" (ANR-18-CE40-0025-01). Euiwong Lee: Simons Collaboration on Algorithms and Geometry.

Acknowledgements

A part of this research was done during the "2019 IBS Summer Research Program on Algorithms and Complexity in Discrete Structures", hosted by the IBS Discrete Mathematics Group.

Cite As Get BibTex

Jungho Ahn, Eun Jung Kim, and Euiwoong Lee. Towards Constant-Factor Approximation for Chordal / Distance-Hereditary Vertex Deletion. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 62:1-62:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.62

Abstract

For a family of graphs ℱ, Weighted ℱ-Deletion is the problem for which the input is a vertex weighted graph G = (V, E) and the goal is to delete S ⊆ V with minimum weight such that G⧵S ∈ 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • ptolemaic
  • approximation algorithm
  • linear programming
  • feedback vertex set

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