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Annals of Operations Research

, Volume 275, Issue 2, pp 259–279 | Cite as

Approximate solutions for expanding search games on general networks

  • Steve Alpern
  • Thomas LidbetterEmail author
Original Research
  • 130 Downloads

Abstract

We study the classical problem introduced by R. Isaacs and S. Gal of minimizing the time to find a hidden point H on a network Q moving from a known starting point. Rather than adopting the traditional continuous unit speed path paradigm, we use the dynamic “expanding search” paradigm recently introduced by the authors. Here the regions S(t) that have been searched by time t are increasing from the starting point and have total length t. Roughly speaking the search follows a sequence of arcs \(a_i\) such that each one starts at some point of an earlier one. This type of search is often carried out by real life search teams in the hunt for missing persons, escaped convicts, terrorists or lost airplanes. The paper which introduced this type of search solved the adversarial problem (where H is hidden to maximize the time to be found) for the cases where Q is a tree or is 2-arc-connected. This paper’s main contribution is to give two strategy classes which can be used on any network and have expected search times which are within a factor close to 1 of the value of the game (minimax search time). These strategies classes are respectively optimal for trees and 2-arc-connected networks. We also solve the game for circle-and-spike networks, which can be considered as the simplest class of networks for which a solution was previously unknown.

Keywords

Search games Zero-sum games Networks Defense and security 

Notes

Acknowledgements

Steve Alpern wishes to acknowledge support from the Air Force Office of Scientific Research [Grant FA9550-14-1-0049].

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Operations Research and Management Science Group, Warwick Business SchoolUniversity of WarwickCoventryUK
  2. 2.Department of Management Science and Information SystemsRutgers Business SchoolNewarkUSA

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