A generative power-law search tree model

Authors:
Alda Carvalho;Nuno Crato;Carla Gomes
Affiliations:
Instituto Superior de Engenharia de Lisboa and Cemapre, Portugal;Cemapre, Institute for Economics and Management, Technical University of Lisbon, Portugal;Cornell University, Ithaca, NY, USA
Venue:
Computers and Operations Research
Year:
2009

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Abstract

It is now a well-established fact that search algorithms can exhibit heavy-tailed behavior. However, the reasons behind this fact are not well understood. We provide a generative search tree model whose distribution of the number of nodes visited during search is formally heavy-tailed. Our model allows us to generate search trees with any degree of heavy-tailedness. We also show how the different regimes observed for the runtime distributions of backtrack search methods across different constrainedness regions of random CSP models can be captured by a mixture of the so-called stable distributions.