Abstract
Jelly-no-Puzzle is a combinatorial puzzle with gravity and colored blocks. It can be considered as a motion planning problem in an environment in which gravity is taken into account. The computational complexity of Jelly-no-Puzzle is studied in this paper. We show that it is NP-complete for one-color, and is NP-hard in the general case.
This work was supported by the Start-up Fund of Guangdong University of Foreign Studies (No. 299-X5219228).
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Notes
- 1.
Jelly no Puzzle is available at http://qrostar.skr.jp/en/jelly/.
- 2.
Hanano Puzzle is available at http://qrostar.skr.jp/en/hanano/.
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Acknowledgements
The author would like to thank the anonymous referees for their very valuable comments which helped to improve this paper, especially for pointing out an error in the original statement of Lemma 1.
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Yang, C. (2021). On the Complexity of Jelly-no-Puzzle. In: Akiyama, J., Marcelo, R.M., Ruiz, MJ.P., Uno, Y. (eds) Discrete and Computational Geometry, Graphs, and Games. JCDCGGG 2018. Lecture Notes in Computer Science(), vol 13034. Springer, Cham. https://doi.org/10.1007/978-3-030-90048-9_13
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