Two Batch Search with weighted Lies
by
Christian Deppe
University of Bielefeld
Coauthors: Rudolf Ahlswede, Ferdinando Cicalese, and Ugo Vaccaro

We consider the problem of searching for an unknown number in the search space U={0, ..., M-1}. q-ary questions can be asked and some of the answers may be wrong. An arbitrary integer weighted bipartite graph G is given, stipulating the cost G(i, j) of each answer j \not = i when the correct answer is i, i.e., the cost of a wrong answer. Correct answers are supposed to be costless. It is assumed that a maximum cost e for the sum of the costs of all wrong answers can be afforded by the responder during the whole game. We provide tight upper and lower bounds for the largest size M = M(q, e, G, 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 in [] and []. The questions in our strategies can be asked in two batches of non adaptive questions. Finally, we remark that our results can be further generalized to a wider class of error models including also unidirectional errors.

Date received: March 19, 2008