A Generator of Heavy-Tailed Search Trees

Abstract

In theoretical computational statistics, the detection of heavy tails in computing costs of some random search algorithms generated an increased interest in the modeling of this heavy-tailed behavior. We propose a general model for these algorithms that reproduces this characteristic. The model represents the search for a solution as the descent of a search tree with regular branching factors and equiprobable nodes. In this work, we present a way to generate heavy-tailed search trees using very simple rules, and we show how a particular case relates to the famous Wallis product.