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Swapping Colored Tokens on Graphs

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Algorithms and Data Structures (WADS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9214))

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Abstract

We investigate the computational complexity of the following problem. We are given a graph in which each vertex has the current and target colors. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and target colors agree at each vertex. When the colors are chosen from \(\{1,2,\dots ,c\}\), we call this problem \(c\) -Colored Token Swapping since the current color of a vertex can be seen as a colored token placed on the vertex. We show that \(c\) -Colored Token Swapping is NP-complete for every constant \(c \ge 3\) even if input graphs are restricted to connected planar bipartite graphs of maximum degree 3. We then show that \(2\) -Colored Token Swapping can be solved in polynomial time for general graphs and in linear time for trees.

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Author information

Authors and Affiliations

  1. Iwate University, Morioka, Japan

    Katsuhisa Yamanaka

  2. Saitama University, Saitama, Japan

    Takashi Horiyama

  3. University of British Columbia, Vancouver, Canada

    David Kirkpatrick

  4. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Yota Otachi & Ryuhei Uehara

  5. Kobe University, Kobe, Japan

    Toshiki Saitoh

  6. Osaka Prefecture University, Sakai, Japan

    Yushi Uno

Authors
  1. Katsuhisa Yamanaka
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  2. Takashi Horiyama
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  3. David Kirkpatrick
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  4. Yota Otachi
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  5. Toshiki Saitoh
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  6. Ryuhei Uehara
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  7. Yushi Uno
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Corresponding author

Correspondence to Katsuhisa Yamanaka .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Carleton University, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. University of Victoria, Victoria, Canada

    Ulrike Stege

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© 2015 Springer International Publishing Switzerland

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Yamanaka, K. et al. (2015). Swapping Colored Tokens on Graphs. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_51

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  • DOI: https://doi.org/10.1007/978-3-319-21840-3_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21839-7

  • Online ISBN: 978-3-319-21840-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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