The search value of a network

The search value of a network Let Q be a connected network with a distinguished (starting) point q0, whose are lengths sum to one. We associate with Q a “search value” V(Q) representing the expected time needed for a searcher, starting at q0 and moving at unit speed, to find a moving hider. We assume neither sees the other until they meet. We demonstrate that the “figure‐eight” network, consisting of two equal loops joined at a central starting point, has a search value not exceeding 15/16. This contradicts a conjecture of Gal that the search value of any network is at least 1. In the other direction, we show that V(Q) ≦ 6kD for a network with k edges and diameter D. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Networks: An International Journal Wiley

The search value of a network

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Publisher
Wiley
Copyright
Copyright © 1985 Wiley Periodicals, Inc., A Wiley Company
ISSN
0028-3045
eISSN
1097-0037
D.O.I.
10.1002/net.3230150208
Publisher site
See Article on Publisher Site

Abstract

Let Q be a connected network with a distinguished (starting) point q0, whose are lengths sum to one. We associate with Q a “search value” V(Q) representing the expected time needed for a searcher, starting at q0 and moving at unit speed, to find a moving hider. We assume neither sees the other until they meet. We demonstrate that the “figure‐eight” network, consisting of two equal loops joined at a central starting point, has a search value not exceeding 15/16. This contradicts a conjecture of Gal that the search value of any network is at least 1. In the other direction, we show that V(Q) ≦ 6kD for a network with k edges and diameter D.

Journal

Networks: An International JournalWiley

Published: Jun 1, 1985

References

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