BibTeX
@MISC{Roy_on“go,
author = {Sudeepa Roy and To The},
title = {ON “GO WITH THE WINNERS”ALGORITHM by},
year = {}
}
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Abstract
Aldous and Vazirani proposed the “Go With The Winners ” algorithm [AV94] to boost the success probability in searching for a leaf at the deepest level � of a search tree, by introducing interactions between simulations. They claim high probability of success using only polynomial (in �) number of simulations (as against the naïve exponential bound) on search trees satisfying certain criteria quantified by a parameter �. This search tree model abstracts the behaviour of Simulated Annealing on a continuous function where a particle moves down to the leaves as the temperature is lowered making irrevocable choices at branch points of the tree. In this work, we propose a simple condition which intends to capture precisely the set of search trees for which the “Go With The Winners ” algorithm will find a deepest node with high probability using only a polynomial number of particles. We show that our condition is both necessary and sufficient for a restricted class of search trees. We conjecture that the same condition precisely captures the set of all search trees for which the “Go With The Winners ” algorithm is efficient. Since our condition is weaker than the sufficient condition as provided in [AV94] for the “Go With The Winners ” algorithm to work, our conjecture, if true, will identify a larger class of search trees, than what the
Keyphrases
search tree go winner algorithm winner algorithm high probability simulated annealing sufficient condition polynomial number deepest node continuous function search tree model success probability na ve exponential bound certain criterion simple condition irrevocable choice branch point restricted class
