Monotonicity and efficient computation of optimal dichotomous search

We consider the problem of designing an efficient dichotomous search in order to locate an object which lies on a given interval. A query at a point of the interval reveals whether the object is to its "left" or to its "right". By successively placing queries at points of the interval it narrows down until the searcher can identify a unit interval containing the object. The objective is to minimize the expected cost of the search. We analyze the problem for a wide range of cost structures, generalizing several known results. In particular we extend a monotonicity theorem of Knuth showing that it also holds under weaker assumptions. Consequently, the computation effort needed to solve the problem is reduced.