IEICE TRANSACTIONS on Fundamentals
On Computational Complexity of Pipe Puzzles
Summary :
In this paper, we investigate computational complexity of pipe puzzles. A pipe puzzle is a kind of tiling puzzle; the input is a set of cards, and a part of a pipe is drawn on each card. For a given set of cards, we arrange them and connect the pipes. We have to connect all pipes without creating any local loop. While ordinary tiling puzzles, like jigsaw puzzles, ask to arrange the tiles with local consistency, pipe puzzles ask to join all pipes. We first show that the pipe puzzle is NP-complete in general even if the goal shape is quite restricted. We also investigate restricted cases and show some polynomial-time algorithms.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.9 pp.1134-1141
- Publication Date
- 2019/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1134
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Puzzles
Authors
Takumu SHIRAYAMA
appci corporation
Takuto SHIGEMURA
The University of Tokyo
Yota OTACHI
Kumamoto University
Shuichi MIYAZAKI
Kyoto University
Ryuhei UEHARA
JAIST
Keyword
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Takumu SHIRAYAMA, Takuto SHIGEMURA, Yota OTACHI, Shuichi MIYAZAKI, Ryuhei UEHARA, "On Computational Complexity of Pipe Puzzles" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 9, pp. 1134-1141, September 2019, doi: 10.1587/transfun.E102.A.1134.
Abstract: In this paper, we investigate computational complexity of pipe puzzles. A pipe puzzle is a kind of tiling puzzle; the input is a set of cards, and a part of a pipe is drawn on each card. For a given set of cards, we arrange them and connect the pipes. We have to connect all pipes without creating any local loop. While ordinary tiling puzzles, like jigsaw puzzles, ask to arrange the tiles with local consistency, pipe puzzles ask to join all pipes. We first show that the pipe puzzle is NP-complete in general even if the goal shape is quite restricted. We also investigate restricted cases and show some polynomial-time algorithms.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1134/_p
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@ARTICLE{e102-a_9_1134,
author={Takumu SHIRAYAMA, Takuto SHIGEMURA, Yota OTACHI, Shuichi MIYAZAKI, Ryuhei UEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Computational Complexity of Pipe Puzzles},
year={2019},
volume={E102-A},
number={9},
pages={1134-1141},
abstract={In this paper, we investigate computational complexity of pipe puzzles. A pipe puzzle is a kind of tiling puzzle; the input is a set of cards, and a part of a pipe is drawn on each card. For a given set of cards, we arrange them and connect the pipes. We have to connect all pipes without creating any local loop. While ordinary tiling puzzles, like jigsaw puzzles, ask to arrange the tiles with local consistency, pipe puzzles ask to join all pipes. We first show that the pipe puzzle is NP-complete in general even if the goal shape is quite restricted. We also investigate restricted cases and show some polynomial-time algorithms.},
keywords={},
doi={10.1587/transfun.E102.A.1134},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - On Computational Complexity of Pipe Puzzles
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1134
EP - 1141
AU - Takumu SHIRAYAMA
AU - Takuto SHIGEMURA
AU - Yota OTACHI
AU - Shuichi MIYAZAKI
AU - Ryuhei UEHARA
PY - 2019
DO - 10.1587/transfun.E102.A.1134
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - In this paper, we investigate computational complexity of pipe puzzles. A pipe puzzle is a kind of tiling puzzle; the input is a set of cards, and a part of a pipe is drawn on each card. For a given set of cards, we arrange them and connect the pipes. We have to connect all pipes without creating any local loop. While ordinary tiling puzzles, like jigsaw puzzles, ask to arrange the tiles with local consistency, pipe puzzles ask to join all pipes. We first show that the pipe puzzle is NP-complete in general even if the goal shape is quite restricted. We also investigate restricted cases and show some polynomial-time algorithms.
ER -
English
