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

doi:10.3390/a5020261

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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

Chuzo Iwamoto* , Kento Sasaki and Kenichi Morita

Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527 Japan

* Author to whom correspondence should be addressed.

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

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Cite This Article

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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