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The Guessing Secrets problem: A probabilistic approach

par Del Lungo, Alberto;Louchard, Guy ;Marini, Claudio;Montagna, Franco
Référence Journal of algorithms, 55, 2, page (142-176)
Publication Publié, 2005-05

Article révisé par les pairs

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Résumé :

We introduce a probabilistic variant of the Guessing Secrets problem proposed by Chung et al. in [Electron. J. Combin. 8 (2001) R13]. In our variation, a player tries to discover the identity of a set S of n unknown secrets drawn by a second player, from a space Ω of N secrets. The first player tries to learn as much as possible about the elements of S by asking binary questions. For each question asked, the second player randomly chooses one of the n secrets of S that he uses in supplying the answer, which in any case must be truthful. We define a simple probabilistic guessing algorithm that allows us to guess all secrets of S with probability one. We show that the expected number of questions needed to guess all secrets is 2n 2log2N and the expected time complexity of the algorithm is script O signO(n2logN). We also propose a generalization of this probabilistic guessing secrets problem, and provide some similar results for this generalization. © 2004 Elsevier Inc. All rights reserved.