Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Find-and-fetch search on a tree

Tools
- Tools
+ Tools

Alpern, Steve (2011) Find-and-fetch search on a tree. Operations Research, Vol.59 (No.5). pp. 1258-1268. doi:10.1287/opre.1110.0966 ISSN 0030-364X.

Research output not available from this repository.

Request-a-Copy directly from author or use local Library Get it For Me service.

Official URL: http://dx.doi.org/10.1287/opre.1110.0966

Request Changes to record.

Abstract

We introduce a new type of search game called the “find-and-fetch” game F(Q, O). The Hider simply picks any point H in the network Q. The Searcher starts at time zero at a given point O of Q, moving at unit speed until he reaches H (finds the Hider). Then he returns at a given speed ρ along the shortest path back to O, arriving at time R, the payoff.

This models the problem faced in many types of search, including search-and-rescue problems and foraging problems of animals (where food must be found and returned to the lair). When Q is a binary tree, we derive optimal probabilities for the Searcher to branch at the nodes. These probabilities give a positive bias towards searching longer branches first. We show that the minimax value of the return time R (the game value of F(Q, O)) is μ + D/ρ, where μ is the total length of Q and D is the mean distance from the root O to the leaves (terminal nodes) of Q, where the mean is taken with respect to what is known as the equal branch density distribution. As ρ goes to infinity, our problem reduces to the search game model where the payoff is simply the time to reach the Hider, and our results tend to those obtained by Gal [Gal, S. 1979. Search games with mobile and immobile hider. SIAM J. Control Optim. 17(1) 99–122] and Anderson and Gal [Anderson, E. J., S. Gal. 1990. Search in a maze. Probab. Engrg. Inform. Sci. 4(3) 311–318] for that model. We also apply our return time formula μ + D/ρ to determine the ideal location for the root (lair or rescue center) O, assuming it can be moved. In the traditional “find only” model, the location of O does not matter.

Item Type: Journal Article
Divisions: Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences
Faculty of Social Sciences > Warwick Business School
Journal or Publication Title: Operations Research
Publisher: Institute for Operations Research and the Management Sciences (I N F O R M S)
ISSN: 0030-364X
Official Date: 2011
Dates:
DateEvent
2011Published
Volume: Vol.59
Number: No.5
Page Range: pp. 1258-1268
DOI: 10.1287/opre.1110.0966
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us