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

Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527 Japan
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Algorithms 2012, 5(2), 261-272; https://doi.org/10.3390/a5020261
Received: 11 November 2011 / Revised: 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 (CC BY 3.0).
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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.

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