Parallel dynamics and computational complexity of the Bak-Sneppen model
Abstract
The parallel computational complexity of the Bak-Sneppen evolution model is studied. It is shown that Bak-Sneppen histories can be generated by a massively parallel computer in a time that is polylogarithmic in the length of the history. In this parallel dynamics, histories are built up via a nested hierarchy of avalanches. Stated in another way, the main result is that the logical depth of producing a Bak-Sneppen history is exponentially less than the length of the history. This finding is surprising because the self-organized critical state of the Bak-Sneppen model has long range correlations in time and space that appear to imply that the dynamics is sequential and history dependent. The parallel dynamics for generating Bak-Sneppen histories is contrasted to standard Bak-Sneppen dynamics. Standard dynamics and an alternate method for generating histories, conditional dynamics, are both shown to be related to P-complete natural decision problems implying that they cannot be efficiently implemented in parallel.
Cite
@article{arxiv.cond-mat/0105296,
title = {Parallel dynamics and computational complexity of the Bak-Sneppen model},
author = {Jon Machta and Xuenan Li},
journal= {arXiv preprint arXiv:cond-mat/0105296},
year = {2009}
}
Comments
37 pages, 12 figures