License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.61
URN: urn:nbn:de:0030-drops-111823
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11182/
Go to the corresponding LIPIcs Volume Portal

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

Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

pdf-format:
LIPIcs-ESA-2019-61.pdf (1 MB)

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.

BibTeX - Entry

@InProceedings{ito_et_al:LIPIcs:2019:11182,
  author =	{Takehiro Ito and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Yoshio Okamoto},
  title =	{{Shortest Reconfiguration of Perfect Matchings via Alternating Cycles}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{61:1--61:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11182},
  URN =		{urn:nbn:de:0030-drops-111823},
  doi =		{10.4230/LIPIcs.ESA.2019.61},
  annote =	{Keywords: Matching, Combinatorial reconfiguration, Alternating cycles, Combinatorial shortest paths}
}

Keywords: Matching, Combinatorial reconfiguration, Alternating cycles, Combinatorial shortest paths
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI