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Parallel dynamics and computational complexity of the Bak-Sneppen model

Jon Machta·Xuenan Li
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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.

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Jon Machta, Xuenan Li. 2001-05-15. Parallel dynamics and computational complexity of the Bak-Sneppen model. https://doi.org/10.1016/s0378-4371(01)00336-3

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