Shortest reconfiguration of perfect matchings via alternating cycles

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.

Original languageEnglish
Title of host publication27th Annual European Symposium on Algorithms, ESA 2019
EditorsMichael A. Bender, Ola Svensson, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771245
DOIs
Publication statusPublished - 2019 Sep
Event27th Annual European Symposium on Algorithms, ESA 2019 - Munich/Garching, Germany
Duration: 2019 Sep 92019 Sep 11

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume144
ISSN (Print)1868-8969

Conference

Conference27th Annual European Symposium on Algorithms, ESA 2019
CountryGermany
CityMunich/Garching
Period19/9/919/9/11

Keywords

  • Alternating cycles
  • Combinatorial reconfiguration
  • Combinatorial shortest paths
  • Matching

ASJC Scopus subject areas

  • Software

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  • Cite this

    Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., & Okamoto, Y. (2019). Shortest reconfiguration of perfect matchings via alternating cycles. In M. A. Bender, O. Svensson, & G. Herman (Eds.), 27th Annual European Symposium on Algorithms, ESA 2019 [61] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 144). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2019.61