The time complexity of permutation routing via matching, token swapping and a variant

Jun Kawahara, Toshiki Saitoh, Ryo Yoshinaka

Research output: Contribution to journalArticlepeer-review


The problems of Permutation Routing via Matching and Token Swapping are reconfiguration problems on graphs. This paper is concerned with the complexity of those problems and a colored variant. For a given graph where each vertex has a unique token on it, those problems requirto find a shortest way to modify a token placement into another by swapping tokens on adjacent vertices. While all pairs of tokens on a matching can be exchanged at once in Permutation Routing via Matching, Token Swapping allows only one pair of tokens can be swapped. In the colored version, vertices and tokens are colored and the goal is to relocate tokenso that each vertex has a token of the same color. We investigate the timcomplexity of several restricted cases of those problems and show when those problems become tractable and remain intractable.

Original languageEnglish
Pages (from-to)29-70
Number of pages42
JournalJournal of Graph Algorithms and Applications
Issue number1
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics


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