A DICHOTOMOUS SEARCH WITH TRAVEL COST

Abstract

An object to be searched is represented by a point in an interval of length n. The searching operation will be started from the left endpoint of the interval. A point at the distance x from the left endpoint will be chosen as the first searching point. It will be assumed that the search at the point finds out whether the object lies to the left or to the right of the point and that a travel cost required to move distance x is ax (a ≧ 0) and a search cost at the point is b (≧ 0) . The problem is that of determining a sequence of searching points so as to minimize the maximum cost required to diminish the existing interval of length n up to unit length, and that of getting the maximum cost required by using this sequence. Furthermore, several properties of minimax policy and considerations of the assumptions are described.