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

5 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 Jan 1
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	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

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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

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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