Year: 2021
Type: preprint
Abstract: In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. In these problems, some tokens are placed on a subset of vertices of the graph, and there are three natural reconfiguration rules called ``token sliding,'' ``token jumping,'' and ``token addition and removal''. In the context of computational complexity of puzzles, the sliding block puzzles play an important role. Depending on the rules and set of pieces, the sliding block puzzles characterize the computational complexity classes including P, NP, and PSPACE. The sliding block puzzles correspond to the token sliding model in the context of combinatorial reconfiguration. On the other hand, a relatively new notion of jumping block puzzles is proposed in puzzle society. This is the counterpart to the token jumping model of the combinatorial reconfiguration problems in the context of block puzzles. We investigate several variants of jumping block puzzles and determine their computational complexities.
Source: arXiv (Cornell University)
Authors: Kanzaki, Masaaki, Otachi, Yota, Uehara, Ryuhei
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Refining the graph parameter hierarchy for fine-grained algorithms, Speeding up FPT algorithms with special tree decompositions, G3429881471, Research on algorithms and data structures for solving theoretically hard problems in practical time, Desigining algorithms for commodities transportation on a planar graph modeling a map, General algorithms for fixed-parameter intractable problems, G8480461622, G908247422
OpenAlex ID: W4299880312