An exponential time parameterized algorithm for planar disjoint paths

Daniel Lokshtanov, Pranabendu Misra, Michal Pilipczuk, Saket Saurabh, Meirav Zehavi

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

3 Scopus citations

Abstract

In the Disjoint Paths problem, the input is an undirected graph G on n vertices and a set of k vertex pairs, {si,ti}i=1k, and the task is to find k pairwise vertex-disjoint paths such that the i'th path connects si to ti. In this paper, we give a parameterized algorithm with running time 2O(k2)nO(1) for Planar Disjoint Paths, the variant of the problem where the input graph is required to be planar. Our algorithm is based on the unique linkage/treewidth reduction theorem for planar graphs by Adler et al. [JCTB 2017], the algebraic co-homology based technique developed by Schrijver [SICOMP 1994] for Disjoint Paths on directed planar graphs, and one of the key combinatorial insights developed by Cygan et al. [FOCS 2013] in their algorithm for Disjoint Paths on directed planar graphs. To the best of our knowledge our algorithm is the first parameterized algorithm to exploit that the treewidth of the input graph is small in a way completely different from the use of dynamic programming.

Original languageEnglish
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
PublisherAssociation for Computing Machinery
Pages1307-1316
Number of pages10
ISBN (Electronic)9781450369794
DOIs
StatePublished - 8 Jun 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: 22 Jun 202026 Jun 2020

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Country/TerritoryUnited States
CityChicago
Period22/06/2026/06/20

Keywords

  • Disjoint paths
  • Homology
  • Network flow
  • Parameterized complexity
  • Planar graphs

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