ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs

Fuente: arXiv
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Main Authors: An, Shinwoo, Oh, Eunjin
Format: Preprint
Published: 2024
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author An, Shinwoo
Oh, Eunjin
author_facet An, Shinwoo
Oh, Eunjin
contents In this paper, we consider the Cycle Packing problem on unit disk graphs 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 $2^{O(\sqrt k)}n^{O(1)}$. This improves the $2^{O(\sqrt k\log k)}n^{O(1)}$-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.
format Preprint
id arxiv_https___arxiv_org_abs_2403_11426
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs
An, Shinwoo
Oh, Eunjin
Data Structures and Algorithms
Computational Geometry
In this paper, we consider the Cycle Packing problem on unit disk graphs 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 $2^{O(\sqrt k)}n^{O(1)}$. This improves the $2^{O(\sqrt k\log k)}n^{O(1)}$-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.
title ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs
topic Data Structures and Algorithms
Computational Geometry
url https://arxiv.org/abs/2403.11426