Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard

Oded Goldreich

doi:10.1007/978-3-642-22670-0_1

Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard

Oded Goldreich

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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.

Original language	English
Title of host publication	Studies in Complexity and Cryptography
Subtitle of host publication	Miscellanea on the Interplay between Randomness and Computation
Editors	Oded Goldreich
Chapter	1
Pages	1-5
Number of pages	5
DOIs	https://doi.org/10.1007/978-3-642-22670-0_1
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6650 LNCS

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-22670-0_1

Cite this

Goldreich, O. (2011). Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard. In O. Goldreich (Ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation (pp. 1-5). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS). https://doi.org/10.1007/978-3-642-22670-0_1

Goldreich, Oded. / Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard. Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. editor / Oded Goldreich. 2011. pp. 1-5 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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year = "2011",

doi = "10.1007/978-3-642-22670-0_1",

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Goldreich, O 2011, Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard. in O Goldreich (ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6650 LNCS, pp. 1-5. https://doi.org/10.1007/978-3-642-22670-0_1

Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard. / Goldreich, Oded.
Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. ed. / Oded Goldreich. 2011. p. 1-5 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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N2 - 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.

AB - 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.

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Goldreich O. Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard. In Goldreich O, editor, Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. 2011. p. 1-5. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22670-0_1

Finding the shortest move-sequence in the graph-generalized 15-puzzle is NP-hard

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