Search Theory: A Differential Equations Approach

Problems of search arise in many contexts that affect people directly and indirectly. Although few of them have searched for submarines or lost hikers, almost all of them at one time have searched for keys or wallets. This chapter introduce search theory from the viewpoint of differential equations, an approach used extensively by 0. Heilman and his students. It shows how various approximate methods, common in applied mathematics, can be used to solve some of the important problems of search theory. The chapter contains derivations of the differential equations of search theory, a formulation of optimal search problems, and a discussion of how the search equations are scaled. It also contains a description of methods used to solve the search equations, either exactly or asymptotically. The chapter then deals with optimal search when one uses effort allocation, and deals with optimal search paths.