The Theory of Search Games and Rendezvous

ISBN-13: 9780792374688 / Angielski / Twarda / 2002 / 319 str.

Steve Alpern; Shmuel Gal; Shmuel Gal

Opis

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.

Spis treści

Preface. Frequently Used Notations. Acknowledgement. Book I: Search Games. 1. Introduction to Search Games. Part One: Search Games in Compact Spaces. 2. General Framework. 3. Search for an Immobile Hider. 4. Search for a Mobile Hider. 5. Miscellaneous Search Games. Part Two: Search Games in Unbounded Domains. 6. General Framework. 7. On Minimax Properties of Geometric Trajectories. 8. Search on the Infinite Line. 9. Star and Plan Search. Book II: Rendezvous Theory. 10. Introduction to Rendezvous Search. 11. Elementary Results and Samples. Part Three: Rendezvous Search on Compact Spaces. 12. Rendezvous Values of a Compact Symmetric Region. 13. Rendezvous on Labeled Networks. 14. Asymmetric Rendezvous on an Unlabeled Circle. 15. Rendezvous on a Graph. Part Four: Rendezvous Search on Unbounded Domains. 16. Asymmetric Rendezvous on the Line (ARPL). 17. Other Rendezvous Problems on the Line. 18. Rendezvous in Higher Dimensions. Appendices. A: A Minimax Theorem for Zero-Sum Games. B: Theory of Alternating Search. C: Rendezvous-Evasion Problems. Bibliography. Index.