Sequentially swapping colored tokens on graphs

Katsuhisa Yamanaka, Erik D. Demaine, Takashi Horiyama, Akitoshi Kawamura, Shin Ichi Nakano, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We consider a puzzle consisting of colored tokens on an nvertex graph, where each token has a distinct starting vertex and a set of allowable target vertices for it to reach, and the only allowed transformation is to “sequentially” move the chosen token along a path of the graph by swapping it with other tokens on the path. This puzzle is a variation of the Fifteen Puzzle and is solvable in O(n3) token-swappings. We thus focus on the problem of minimizing the number of token-swappings to reach the target token-placement. We first give an inapproximability result of this problem, and then show polynomial-time algorithms on trees, complete graphs, and cycles.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
EditorsMd. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon
PublisherSpringer Verlag
Pages435-447
Number of pages13
ISBN (Print)9783319539249
DOIs
Publication statusPublished - Jan 1 2017
Externally publishedYes
Event11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China
Duration: Mar 29 2017Mar 31 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10167 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
CountryTaiwan, Province of China
CityHsinchu
Period3/29/173/31/17

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Yamanaka, K., Demaine, E. D., Horiyama, T., Kawamura, A., Nakano, S. I., Okamoto, Y., Saitoh, T., Suzuki, A., Uehara, R., & Uno, T. (2017). Sequentially swapping colored tokens on graphs. In M. S. Rahman, H-C. Yen, & S-H. Poon (Eds.), WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings (pp. 435-447). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10167 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-53925-6_34