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DOI: 10.4230/LIPIcs.ESA.2019.61
URN: urn:nbn:de:0030-drops-111823
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11182/
Ito, Takehiro ; Kakimura, Naonori ; Kamiyama, Naoyuki ; Kobayashi, Yusuke ; Okamoto, Yoshio
Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
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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 | |
| Seminar: | 27th Annual European Symposium on Algorithms (ESA 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 06.09.2019 |
