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Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

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

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Matching
  • Combinatorial reconfiguration
  • Alternating cycles
  • Combinatorial shortest paths

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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.

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Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto. Shortest Reconfiguration of Perfect Matchings via Alternating Cycles. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 61:1-61:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ESA.2019.61

Author Details

Takehiro Ito
  • Tohoku University, Sendai, Japan
Naonori Kakimura
  • Keio University, Yokohama, Japan
Naoyuki Kamiyama
  • Kyushu University, Fukuoka, Japan
  • JST, PRESTO, Kawaguchi, Japan
Yusuke Kobayashi
  • Kyoto University, Kyoto, Japan
Yoshio Okamoto
  • University of Electro-Communications, Chofu, Japan
  • RIKEN Center for Advanced Intelligence Project, Tokyo, Japan

Funding

  • Ito, Takehiro: Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan.
  • Kakimura, Naonori: Partially supported by JSPS KAKENHI Grant Numbers JP17K00028 and JP18H05291, Japan.
  • Kamiyama, Naoyuki: Partially supported by JST PRESTO Grant Number JPMJPR1753, Japan.
  • Kobayashi, Yusuke: Partly supported by JSPS KAKENHI Grant Numbers JP16K16010, JP17K19960, and JP18H05291, Japan.
  • Okamoto, Yoshio: Partially supported by JSPS KAKENHI Grant Number 15K00009 and JST CREST Grant Number JPMJCR1402, and Kayamori Foundation of Informational Science Advancement.

References

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