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Algorithms 2012, 5(2), 261-272; doi:10.3390/a5020261
Article

A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem

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Received: 11 November 2011; in revised form: 27 February 2012 / Accepted: 7 April 2012 / Published: 13 April 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
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Abstract: A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A string puzzle consists of strings entangled with one or more wooden pieces. We consider the generalized string puzzle problem whose input is the layout of strings and a wooden board with holes embedded in the 3-dimensional Euclidean space. We present a polynomial-time transformation from an arbitrary instance ƒ of the 3SAT problem to a string puzzle s such that ƒ is satisfiable if and only if s is solvable. Therefore, the generalized string puzzle problem is NP-hard.
Keywords: disentanglement puzzle; polynomial-time reduction; NP-hard disentanglement puzzle; polynomial-time reduction; NP-hard
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Iwamoto, C.; Sasaki, K.; Morita, K. A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem. Algorithms 2012, 5, 261-272.

AMA Style

Iwamoto C, Sasaki K, Morita K. A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem. Algorithms. 2012; 5(2):261-272.

Chicago/Turabian Style

Iwamoto, Chuzo; Sasaki, Kento; Morita, Kenichi. 2012. "A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem." Algorithms 5, no. 2: 261-272.


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