On the algorithmic complexity of the Mastermind game with black-peg results

In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-co...

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Veröffentlicht in:Information processing letters Jg. 109; H. 13; S. 675 - 678
1. Verfasser: Goodrich, Michael T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 15.06.2009
Elsevier
Elsevier Sequoia S.A
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Genetics
Information processing
Mastermind
Miscellaneous
NP-completeness
Studies
Theoretical computing
Mastermind
Algorithms
NP-completeness
Computer theory
Query
Color
Algorithmics
Algorithm
Completeness
Algorithm complexity
Information processing
Genetics
Application
Vector
Algorithm analysis
ISSN:0020-0190, 1872-6119
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Zusammenfassung:In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms for discovering a hidden vector through single-color queries. Indeed, our algorithm improves a previous method of Chvátal by almost a factor of 2.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2009.02.021