Coping with delays and time-outs in binary search procedures?

Abstract

How many questions are necessary 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?", when answers are received with a constant delay d; and up to a constant number c of the answers can be lost, i.e. can be not received at all? We exactly solve this problem for all integers d ³0 and c = 1: We also briefly discuss the analogy between the above problem and that of broadcasting over a fully connected network with link latency.