Two batch search with lie cost

  • Authors:

  • Rudolf Ahlswede;Ferdinando Cicalese;Christian Deppe;Ugo Vaccaro

  • Affiliations:

  • Department of Mathematics, Bielefeld University, Bielefeld, Germany;Department of Computer Science and Applications, University of Salerno, Baronissi, SA, Italy;Department of Mathematics, Bielefeld University, Bielefeld, Germany;Department of Computer Science and Applications, University of Salerno, Baronissi, SA, Italy

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

We consider the problem of searching for an unknown number in the search space u = {0,..., M -1}. qary questions can be asked and some of the answers may be wrong. An arbitrary integer weighted bipartite graph Γ is given, stipulating the cost Γ(i,j) of each answer j ≠ i when the correct answer is i, i.e., the cost of a wrong answer. Correct answers are supposed to be cost-less. It is assumed that a maximum cost e for the sum of the cost of all wrong answers can be afforded by the responder during the whole search. We provide tight upper and lower bounds for the largest size M = M (q, e, Γ, n) for which it is possible to find an unknown number x* ∈ u with n q-ary questions and maximum lie cost e. Our results improve the bounds of Cicalese et al. (2004) and Ahlswede et al. (2008). The questions in our strategies can be asked in two batches of nonadaptive questions. Finally, we remark that our results can be further generalized to a wider class of error models including also unidirectional errors.