TY - GEN

T1 - Sequentially Swapping Tokens

T2 - 48th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2023

AU - Kiya, Hironori

AU - Okada, Yuto

AU - Ono, Hirotaka

AU - Otachi, Yota

N1 - Funding Information:
Partially supported by JSPS KAKENHI Grant Numbers JP17H01698, JP17K19960, JP18H04091, JP20H05793, JP20H05967, JP21K11752, JP21K19765, JP21K21283, JP22H00513. The full version is available at https://arxiv.org/abs/2210.02835.
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king’s graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.

AB - We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king’s graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.

UR - http://www.scopus.com/inward/record.url?scp=85146674440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85146674440&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-23101-8_15

DO - 10.1007/978-3-031-23101-8_15

M3 - Conference contribution

AN - SCOPUS:85146674440

SN - 9783031231001

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 222

EP - 235

BT - SOFSEM 2023

A2 - Gasieniec, Leszek

PB - Springer Science and Business Media Deutschland GmbH

Y2 - 15 January 2023 through 18 January 2023

ER -