Improved approximation algorithm for the number of queries necessary to identify a permutation

Abstract

In the past three decades, deductive games have become interesting from the algorithmic point of view. A well known deductive game is the famous Mastermind game. In this paper, we consider the so called Black-Peg variant of Mastermind. More precisely, we deal with a special version of the Black-Peg game with n holes and k ≥ n colors where no repetition of colors is allowed. We present a strategy that identifies the secret code in O(n log2 n) queries. Our algorithm improves the previous result of Ker-I Ko and Shia-Chung Teng (1986) by almost a factor of 2 for the case k = n. To our knowledge there is no previous work dealing with the case k > n. © 2013 Springer-Verlag.