Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2005-14

October 2005

How to Search a Tree to which Eulerian Networks are Attached

Steve Alpern

We call a network partly Eulerian if consists of a tree (of length a and radius r) to which a finite number of disjoint Eulerian networks (of total length b) are attached, each at a single point. We show that for such networks, a search strategy consisting equiprobably of a minimal (Chinese Postman) covering path and its reverse path is optimal, in the sense that it minimizes (at a + b/2 - r) the expected time to find a point hidden according to the worst case distribution. This generalizes a similar result of Dagan and Gal for search games on trees.

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Last modified: 31 October 2005