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

doi:10.1007/978-3-319-53925-6_34

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

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 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 language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
Editors	Md. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon
Publisher	Springer Verlag
Pages	435-447
Number of pages	13
ISBN (Print)	9783319539249
DOIs	https://doi.org/10.1007/978-3-319-53925-6_34
Publication status	Published - 2017
Event	11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China Duration: 2017 Mar 29 → 2017 Mar 31

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10167 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
Country/Territory	Taiwan, Province of China
City	Hsinchu
Period	17/3/29 → 17/3/31

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-53925-6_34

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

Sequentially swapping colored tokens on graphs. / Yamanaka, Katsuhisa; Demaine, Erik D.; Horiyama, Takashi; Kawamura, Akitoshi; Nakano, Shin Ichi; Okamoto, Yoshio; Saitoh, Toshiki; Suzuki, Akira; Uehara, Ryuhei; Uno, Takeaki.

WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. ed. / Md. Saidur Rahman; Hsu-Chun Yen; Sheung-Hung Poon. Springer Verlag, 2017. p. 435-447 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10167 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yamanaka, K, Demaine, ED, Horiyama, T, Kawamura, A, Nakano, SI, Okamoto, Y, Saitoh, T, Suzuki, A, Uehara, R & Uno, T 2017, Sequentially swapping colored tokens on graphs. in MS Rahman, H-C Yen & S-H Poon (eds), WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10167 LNCS, Springer Verlag, pp. 435-447, 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017, Hsinchu, Taiwan, Province of China, 17/3/29. https://doi.org/10.1007/978-3-319-53925-6_34

Yamanaka K, Demaine ED, Horiyama T, Kawamura A, Nakano SI, Okamoto Y et al. Sequentially swapping colored tokens on graphs. In Rahman MS, Yen H-C, Poon S-H, editors, WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. Springer Verlag. 2017. p. 435-447. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-53925-6_34

Yamanaka, Katsuhisa ; Demaine, Erik D. ; Horiyama, Takashi ; Kawamura, Akitoshi ; Nakano, Shin Ichi ; Okamoto, Yoshio ; Saitoh, Toshiki ; Suzuki, Akira ; Uehara, Ryuhei ; Uno, Takeaki. / Sequentially swapping colored tokens on graphs. WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. editor / Md. Saidur Rahman ; Hsu-Chun Yen ; Sheung-Hung Poon. Springer Verlag, 2017. pp. 435-447 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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N2 - 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.

AB - 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.

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Sequentially swapping colored tokens on graphs

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