Finding, hitting and packing cycles in subexponential time on unit disk graphs

Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

We give algorithms with running time 2O(√κ log κ)· nO(1) for the following problems. Given an n-vertex unit disk graph G and an integer k, decide whether G contains a path on exactly/at least k vertices, a cycle on exactly κ vertices, a cycle on at least k vertices, a feedback vertex set of size at most k, and a set of κ pairwise vertex-disjoint cycles. For the first three problems, no subexponential time parameterized algorithms were previously known. For the remaining two problems, our algorithms significantly outperform the previously best known parameterized algorithms that run in time 2O(κ0.75 log κ)· nO(1). Our algorithms are based on a new kind of tree decompositions of unit disk graphs where the separators can have size up to kO(1) and there exists a solution that crosses every separator at most O(√κ) times. The running times of our algorithms are optimal up to the log k factor in the exponent, assuming the Exponential Time Hypothesis.

Original languageEnglish
Title of host publication44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
EditorsAnca Muscholl, Piotr Indyk, Fabian Kuhn, Ioannis Chatzigiannakis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770415
DOIs
StatePublished - 1 Jul 2017
Externally publishedYes
Event44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 - Warsaw, Poland
Duration: 10 Jul 201714 Jul 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume80
ISSN (Print)1868-8969

Conference

Conference44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
Country/TerritoryPoland
CityWarsaw
Period10/07/1714/07/17

Keywords

  • Cycle packing
  • Feedback vertex set
  • Longest cycle
  • Parameterized complexity
  • Unit disk graph

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