Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

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

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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

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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)


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.

Subject Classification

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


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