English

On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results

Data Structures and Algorithms 2009-05-13 v1 Computational Complexity

Abstract

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 Chvatal by almost a factor of 2.

Keywords

Cite

@article{arxiv.0904.4911,
  title  = {On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results},
  author = {Michael T. Goodrich},
  journal= {arXiv preprint arXiv:0904.4911},
  year   = {2009}
}

Comments

Expanded version with a figure showing the Mastermind game