Feedback Vertex Set on Geometric Intersection Graphs

Authors Shinwoo An, Eunjin Oh

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Shinwoo An
  • POSTECH, Pohang, South Korea
Eunjin Oh
  • POSTECH, Pohang, South Korea

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Shinwoo An and Eunjin Oh. Feedback Vertex Set on Geometric Intersection Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 47:1-47:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time 2^O(√k)(n+m), where n and m denote the numbers of vertices and edges, respectively. This improves the 2^O(√klog k) n^O(1)-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis. Also, our algorithm can be extended to handle geometric intersection graphs of similarly sized fat objects without increasing the running time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Feedback vertex set
  • intersection graphs
  • parameterized algorithm


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