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

Fingerprint

Computational complexity
Polynomials

Keywords

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

ASJC Scopus subject areas

  • Software

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

Shortest reconfiguration of perfect matchings via alternating cycles. / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio.

27th Annual European Symposium on Algorithms, ESA 2019. ed. / Michael A. Bender; Ola Svensson; Grzegorz Herman. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 61 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 144).

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

Ito, T, Kakimura, N, Kamiyama, N, Kobayashi, Y & Okamoto, Y 2019, Shortest reconfiguration of perfect matchings via alternating cycles. in MA 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, 27th Annual European Symposium on Algorithms, ESA 2019, Munich/Garching, Germany, 19/9/9. https://doi.org/10.4230/LIPIcs.ESA.2019.61
Ito T, Kakimura N, Kamiyama N, Kobayashi Y, Okamoto Y. Shortest reconfiguration of perfect matchings via alternating cycles. In Bender MA, Svensson O, Herman G, editors, 27th Annual European Symposium on Algorithms, ESA 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 61. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ESA.2019.61
Ito, Takehiro ; Kakimura, Naonori ; Kamiyama, Naoyuki ; Kobayashi, Yusuke ; Okamoto, Yoshio. / Shortest reconfiguration of perfect matchings via alternating cycles. 27th Annual European Symposium on Algorithms, ESA 2019. editor / Michael A. Bender ; Ola Svensson ; Grzegorz Herman. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).
@inproceedings{2256a918b19b46cb976e95218f6cde51,
title = "Shortest reconfiguration of perfect matchings via alternating cycles",
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.",
keywords = "Alternating cycles, Combinatorial reconfiguration, Combinatorial shortest paths, Matching",
author = "Takehiro Ito and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Yoshio Okamoto",
year = "2019",
month = "9",
doi = "10.4230/LIPIcs.ESA.2019.61",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Bender, {Michael A.} and Ola Svensson and Grzegorz Herman",
booktitle = "27th Annual European Symposium on Algorithms, ESA 2019",

}

TY - GEN

T1 - Shortest reconfiguration of perfect matchings via alternating cycles

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Okamoto, Yoshio

PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

KW - Alternating cycles

KW - Combinatorial reconfiguration

KW - Combinatorial shortest paths

KW - Matching

UR - http://www.scopus.com/inward/record.url?scp=85074837915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074837915&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ESA.2019.61

DO - 10.4230/LIPIcs.ESA.2019.61

M3 - Conference contribution

AN - SCOPUS:85074837915

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 27th Annual European Symposium on Algorithms, ESA 2019

A2 - Bender, Michael A.

A2 - Svensson, Ola

A2 - Herman, Grzegorz

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -