Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.33
URN: urn:nbn:de:0030-drops-133773
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13377/
Hamersma, Joep ; van Kreveld, Marc ; Uno, Yushi ; van der Zanden, Tom C.
Gourds: A Sliding-Block Puzzle with Turning
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Abstract
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1×2 pieces on a hexagonal grid board of 2n+1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.
BibTeX - Entry
@InProceedings{hamersma_et_al:LIPIcs:2020:13377,
author = {Joep Hamersma and Marc van Kreveld and Yushi Uno and Tom C. van der Zanden},
title = {{Gourds: A Sliding-Block Puzzle with Turning}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {33:1--33:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-173-3},
ISSN = {1868-8969},
year = {2020},
volume = {181},
editor = {Yixin Cao and Siu-Wing Cheng and Minming Li},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13377},
URN = {urn:nbn:de:0030-drops-133773},
doi = {10.4230/LIPIcs.ISAAC.2020.33},
annote = {Keywords: computational complexity, divide-and-conquer, Hamiltonian cycle, puzzle game, (combinatorial) reconfiguration, sliding-block puzzle}
}
| Keywords: | computational complexity, divide-and-conquer, Hamiltonian cycle, puzzle game, (combinatorial) reconfiguration, sliding-block puzzle | |
| Seminar: | 31st International Symposium on Algorithms and Computation (ISAAC 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
