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ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs

Authors Shinwoo An, Eunjin Oh

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Author Details

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

Funding

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (No.RS-2023-00209069).

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Shinwoo An and Eunjin Oh. ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.7

Abstract

In this paper, we consider the Cycle Packing problem on a unit disk graph defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of k vertex-disjoint cycles of G if it exists. Our algorithm runs in time 2^O(√k) n^O(1). This improves the 2^O(√klog k) n^O(1)-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Unit disk graphs
  • cycle packing
  • tree decomposition
  • parameterized algorithm

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References

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