Phase Transition in a Random Fragmentation Problem with Applications to Computer Science
Abstract
We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.
Cite
@article{arxiv.cond-mat/0205034,
title = {Phase Transition in a Random Fragmentation Problem with Applications to Computer Science},
author = {David S. Dean and Satya N. Majumdar},
journal= {arXiv preprint arXiv:cond-mat/0205034},
year = {2009}
}
Comments
5 pages RevTeX, 3 figures (.eps)