Finding the Shortest Move-Sequence in the Graph-Generalized 15-Puzzle Is NP-Hard

Following Wilson (J. Comb. Th. (B), 1975), Johnson (J. of Alg., 1983), and Kornhauser, Miller and Spirakis (25th FOCS, 1984), we consider a game that consists of moving distinct pebbles along the edges of an undirected graph. At most one pebble may reside in each vertex at any time, and it is only a...

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Bibliographic Details
Published inStudies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation pp. 1 - 5
Main Author Goldreich, Oded
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2011
SeriesLecture Notes in Computer Science
Subjects
Computational Group Theory
Games’ Complexity
NP-Completeness
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Summary:Following Wilson (J. Comb. Th. (B), 1975), Johnson (J. of Alg., 1983), and Kornhauser, Miller and Spirakis (25th FOCS, 1984), we consider a game that consists of moving distinct pebbles along the edges of an undirected graph. At most one pebble may reside in each vertex at any time, and it is only allowed to move one pebble at a time (which means that the pebble must be moved to a previously empty vertex). We show that the problem of finding the shortest sequence of moves between two given “pebble configuations” is NP-Hard.
ISBN:3642226698
9783642226694
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-22670-0_1