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#1 Estimating the size of search trees by sampling with domain knowledge [PDF] [Copy] [Kimi] [REL]

Authors: Gleb Belov ; Samuel Esler ; Dylan Fernando ; Pierre Le Bodic ; George L. Nemhauser

We show how recently-defined abstract models of the Branch-and-Bound algorithm can be used to obtain information on how the nodes are distributed in B&B search trees. This can be directly exploited in the form of probabilities in a sampling algorithm given by Knuth that estimates the size of a search tree. This method reduces the offline estimation error by a factor of two on search trees from Mixed-Integer Programming instances.