The Theory of Search Games and Rendezvous (International Series in Operations Research & Management Science (55))

Search Theory is one of the original disciplines within the field of Operations Research. It deals with the problem faced by a Searcher who wishes to minimize the time required to find a hidden object, or “target. ” The Searcher chooses a path in the “search space” and finds the target when he is sufficiently close to it. Traditionally, the target is assumed to have no motives of its own regarding when it is found; it is simply stationary and hidden according to a known distribution (e. g. , oil), or its motion is determined stochastically by known rules (e. g. , a fox in a forest). The problems dealt with in this book assume, on the contrary, that the “target” is an independent player of equal status to the Searcher, who cares about when he is found. We consider two possible motives of the target, and divide the book accordingly. Book I considers the zero-sum game that results when the target (here called the Hider) does not want to be found. Such problems have been called Search Games (with the “ze- sum” qualifier understood). Book II considers the opposite motive of the target, namely, that he wants to be found. In this case the Searcher and the Hider can be thought of as a team of agents (simply called Player I and Player II) with identical aims, and the coordination problem they jointly face is called the Rendezvous Search Problem. Front Matter....Pages i-xv Front Matter....Pages 1-1 Introduction to Search Games....Pages 3-6 Front Matter....Pages 7-7 General Framework....Pages 9-12 Search for an Immobile Hider....Pages 13-43 Search for a Mobile Hider....Pages 45-77 Miscellaneous Search Games....Pages 79-97 Front Matter....Pages 99-99 General Framework....Pages 101-105 On Minimax Properties of Geometric Trajectories....Pages 107-122 Search on the Infinite Line....Pages 123-144 Star and Plan Search....Pages 145-162 Front Matter....Pages 163-163 Introduction to Rendezvous Search....Pages 165-172 Elementary Results and Examples....Pages 173-178 Front Matter....Pages 179-179 Rendezvous Values of a Compact Symmetric Region....Pages 181-189 Rendezvous on Labeled Networks....Pages 191-205 Asymmetric Rendezvous on an Unlabeled Circle....Pages 207-221 Rendezvous on a Graph....Pages 223-234 Front Matter....Pages 235-235 Asymmetric Rendezvous on the Line (ARPL)....Pages 237-249 Other Rendezvous Problems on the Line....Pages 251-275 Rendezvous in Higher Dimensions....Pages 277-290 Back Matter....Pages 291-319 The Theory of Search Games and Rendezvous widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found. These multiple motives of searcher and hider are analytically and mathematically considered in the book's two foci: Search Games (Book I) and Rendezvous Theory (Book II). Shmuel Gal's work on Search Games (Gal, 1980) stimulated considerable research in a variety of fields including Computer Science, Engineering, Biology, and Economics. Steve Alpern's original formulation of the rendezvous search problem in 1976 and his formalization of the continuous version (Alpern, 1995) have led to much research in rendezvous theory in the past few years. New material is covered in both Search Games (Book I) and Rendezvous Theory (Book II). The book examines a whole variety of new configurations of theory and problems that arise from these two aspects of the analysis - resulting in a penetrating state-of-the-art treatment of this highly useful mathematical, analytical tool "Traditionally, the target of the search is assigned to have no motives of its own and is either stationary (e.g., oil, network problems, etc.) or its motion is determined stochastically by known rules (e.g., financial markets, scheduling, genetics, etc.). The theory of search games and rendezvous widens the dimensions to the classical problem with the addition of an independent player of equal status to the searcher, who cares about being found or not being found. These multiple motives of searcher and hider are analytically and mathematically considered the book's two foci: Search Games (Book I) and Rendezvous Theory (Book II)." "The book examines a whole variety of new configurations of theory and problems that arise from these two aspects of the analysis - resulting in a penetrating state-of-the-art treatment of this highly useful mathematical, analytical tool."--BOOK JACKET.

Exploring a specialized area of operations research, Alpern (London School of Economics, UK) and Gal (U. of Haifa, Israel) consider the mathematical study of search games, considering zero-sum search games in which targets are seeking not to found by the hider and the opposite case (called the rendezvous search problem) in which the target seeks to found. They examine both classical and new results in research. Annotation (c)2003 Book News, Inc., Portland, OR

In this book we are mainly concerned with finding an "optimal" search trajectory for detecting a target.