A simple proof that the (n2 − 1)-puzzle is hard
Name
1707.03146.pdf
Description
Submitted version
Size
351.54 KB
Format
Unknown
Checksum (MD5)
f309610fc9f269931420a4c320128f30
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.TCS.2018.04.031
