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

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

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 lay...

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Bibliographic Details
Main Authors: Kenichi Morita, Chuzo Iwamoto, Kento Sasaki
Format: Article
Language:English
Published: MDPI AG 2012-04-01
Series:Algorithms
Subjects:
disentanglement puzzle
polynomial-time reduction
NP-hard
Online Access:http://www.mdpi.com/1999-4893/5/2/261/
Description
Summary: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.
ISSN:1999-4893

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