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Shortest Reconfiguration of Sliding Tokens on a Caterpillar

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WALCOM: Algorithms and Computation (WALCOM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9627))

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Abstract

For given two independent sets \({\mathbf I}_b\) and \({\mathbf I}_r\) of a graph, the sliding token problem is to determine if there exists a sequence of independent sets which transforms \({\mathbf I}_b\) into \({\mathbf I}_r\) so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph. The sliding token problem is one of the reconfiguration problems that attract the attention from the viewpoint of theoretical computer science. These problems tend to be PSPACE-complete in general, and some polynomial time algorithms are shown in restricted cases. Recently, the problems for finding a shortest reconfiguration sequence are investigated. For the 3SAT reconfiguration problem, a trichotomy for the complexity of finding the shortest sequence has been shown; it is in P, NP-complete, or PSPACE-complete in certain conditions. Even if it is polynomial time solvable to decide whether two instances are reconfigured with each other, it can be NP-complete to find a shortest sequence between them. We show nontrivial polynomial time algorithms for finding a shortest sequence between two independent sets for some graph classes. As far as the authors know, one of them is the first polynomial time algorithm for the shortest sliding token problem that requires detours of tokens.

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Notes

  1. 1.

    In this paper, a bold \({\mathbf I}\) denotes an “independent set,” an italic I denotes an “interval,” and calligraphy \(\mathcal{I}\) denotes “a set of intervals.”.

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Authors and Affiliations

  1. School of Information Science, JAIST, Nomi, Ishikawa, Japan

    Takeshi Yamada & Ryuhei Uehara

Authors
  1. Takeshi Yamada
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  2. Ryuhei Uehara
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Correspondence to Ryuhei Uehara .

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Editors and Affiliations

  1. Dept. of Computer Science and Engin., Bangladesh Univ. of Engin. & Technol., Dhaka, Bangladesh

    Mohammad Kaykobad

  2. Dept. of Computer Science, Sapienza University of Rome, Rome, Italy

    Rossella Petreschi

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Yamada, T., Uehara, R. (2016). Shortest Reconfiguration of Sliding Tokens on a Caterpillar. In: Kaykobad, M., Petreschi, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2016. Lecture Notes in Computer Science(), vol 9627. Springer, Cham. https://doi.org/10.1007/978-3-319-30139-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-30139-6_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30138-9

  • Online ISBN: 978-3-319-30139-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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