Parallel Dynamics and Computational Complexity of Network Growth Models

Details Parallel Dynamics and Computational Complexity of Network Growth Models Parallel Dynamics and Computational Complexity of Network Growth Models

2004-08-16

arxiv.org/abs/cond-mat/0408372v2

Phys. Rev. E71, 026704 (2005)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 figures

Scientific paper

10.1103/PhysRevE.71.026704

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a power, $\alpha$ of the connectivity of the existing node. Algorithms for generating growing networks very quickly in parallel are described and studied. The sublinear and superlinear cases require distinct algorithms. As a result, there is a discontinuous transition in the parallel complexity of sampling these networks corresponding to the discontinuous structural transition at $\alpha=1$, where the networks become scale free. For $\alpha>1$ networks can be generated in constant time while for $0 \leq \alpha < 1$ logarithmic parallel time is required. The results show that these networks have little depth and embody very little history dependence despite being defined by sequential growth rules.

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