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Searches on a Binary Tree with Random Edge-Weights

Published online by Cambridge University Press:  01 November 1999

ALAN STACEY
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England (e-mail: a.m.stacey@dpmms.cam.ac.uk)

Abstract

Each edge of the standard rooted binary tree is equipped with a random weight; weights are independent and identically distibuted. The value of a vertex is the sum of the weights on the path from the root to the vertex. We wish to search the tree to find a vertex of large weight. A very natural conjecture of Aldous states that, in the sense of stochastic domination, an obvious greedy algorithm is best possible. We show that this conjecture is false. We prove, however, that in a weaker sense there is no significantly better algorithm.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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