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29 March 2024
 
  » arxiv » cond-mat/9403006

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The Parallel Complexity of Growth Models
J. Machta ; R. Greenlaw ;
Date 1 Mar 1994
Journal J. Stat. Phys. 77 (1994) 755
Subject cond-mat
AbstractThis paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale as $O(log^2 N)$, where $N$ is the system size, and the number of processors required scale as a polynomial in $N$. The algorithms are based on fast parallel procedures for finding minimum weight paths; they illuminate the close connection between growth models and self-avoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such as diffusion-limited aggregation, for which fast parallel algorithms probably do not exist.
Source arXiv, cond-mat/9403006
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