THE GENERALIZED LINEAR SEARCH PROBLEM, EXISTENCE OF OPTIMAL SEARCH PATHS

Abstract

A target x is a point on the real line given by the value of a random variable X, which has some distribution function F. A searcher starts looking for x from some point on the line, using a continuous path. He makes for x with un upper bound on his speed till he finds it. The target being sought for might be in either direction from the starting point, so the searcher has in general to retrace his steps many times before he attains his goal. It is desired to search in an optimal manner so as to minimize the expected cost of the search. All previous papers treated this problem using the origin as the starting point of the search. They have been proved that one can minimize the expected cost if the underlying distribution satisfies certain conditions. In this paper, the problem will be treated in the "General Case", which means that the search may start from any point on the real line. Conditions under which we can minimize the expected cost in the general case will be given.