A simple proof that the (n2 − 1)-puzzle is hard

Demaine, Erik D; Rudoy, Mikhail

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A simple proof that the (n2 − 1)-puzzle is hard

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Author(s)

Demaine, Erik D

•

Rudoy, Mikhail

Date Issued

2018

Journal

Theoretical Computer Science

Publisher

Elsevier BV

Version

Original manuscript

Abstract

© 2018 Elsevier B.V. The 15 puzzle is a classic reconfiguration puzzle with fifteen uniquely labeled unit squares within a 4×4 board in which the goal is to slide the squares (without ever overlapping) into a target configuration. By generalizing the puzzle to an n×n board with n2−1 squares, we can study the computational complexity of problems related to the puzzle; in particular, we consider the problem of determining whether a given end configuration can be reached from a given start configuration via at most a given number of moves. This problem was shown NP-complete in [1]. We provide an alternative simpler proof of this fact by reduction from the rectilinear Steiner tree problem.

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Creative Commons Attribution-NonCommercial-NoDerivs License

http://creativecommons.org/licenses/by-nc-nd/4.0/

Persistent DSpace Link

https://hdl.handle.net/1721.1/134978

DOI of Published Version

10.1016/J.TCS.2018.04.031