Binary search with delayed and missing answers

Authors:
Ferdinando Cicalese;Ugo Vaccaro
Affiliations:
Dipartimento di Informatica ed Applicazioni, University of Salerno, 84081 Baronissi (SA), Italy;Dipartimento di Informatica ed Applicazioni, University of Salerno, 84081 Baronissi (SA), Italy
Venue:
Information Processing Letters
Year:
2003

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Abstract

How many questions are necessary and sufficient to guess an unknown number x in the set S = {1, 2 ..... n}, by using only comparison questions, that is questions of the type "Is x ≤ a?", a ∈ S, when answers to questions are received with a delay of d time units and up to c of the answers can be lost, i.e., can not be received at all? We exactly solve this problem for all integers d ≥ and c= 1.