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Maximum Independent Sets in Disk Graphs with Disks in Convex Position

Authors Anastasiia Tkachenko , Haitao Wang

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LIPIcs.SWAT.2026.40.pdf
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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
Keywords
  • disk graphs
  • independent sets
  • convex position
  • dispersion

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Abstract

For a set 𝒟 of disks in the plane, its disk graph G(𝒟) is the graph with vertex set 𝒟, where two vertices are adjacent if and only if the corresponding disks intersect. Given a set 𝒟 of n weighted disks, computing a maximum independent set of G(𝒟) is NP-hard. In this paper, we present an O(n³log n)-time algorithm for this problem in a special setting in which the disks are in convex position, meaning that every disk appears on the convex hull of 𝒟. This setting has been studied previously for disks of equal radius, for which an O(n^{37/11})-time algorithm was known. Our algorithm also works in the weighted case where disks have weights and the goal is to compute a maximum-weight independent set. As an application of our result, we obtain an O(n³log² n)-time algorithm for the dispersion problem on a set of n disks in convex position: given an integer k, compute a subset of k disks that maximizes the minimum pairwise distance among all disks in the subset.

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Anastasiia Tkachenko and Haitao Wang. Maximum Independent Sets in Disk Graphs with Disks in Convex Position. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.40

Author Details

Anastasiia Tkachenko
  • Kahlert School of Computing, University of Utah, Salt Lake City, UT, USA
Haitao Wang
  • Kahlert School of Computing, University of Utah, Salt Lake City, UT, USA

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