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Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set

Authors Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Computational geometry
Keywords
  • Subexponential FPT algorithms
  • geometric intersection graphs

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Abstract

The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph G and a parameter k, one has to decide if there is a set S of at most k vertices such that G-S is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time 2^{o(k)}n^{𝒪(1)} in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such 2^{o(k)}n^{𝒪(1)} algorithms. 
In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time 2^k^ε poly(n), for some ε < 1, where n denotes the number of vertices of the instance and k the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of "thin" objects like segment graphs or more generally s-string graphs.

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Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.26

Author Details

Gaétan Berthe
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Marin Bougeret
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Daniel Gonçalves
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Jean-Florent Raymond
  • CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP, UMR5668, Lyon, France

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