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Parallel Dynamics and Computational Complexity of Network Growth Models | | Benjamin Machta
; Jonthan Machta
; | | Date: |
16 Aug 2004 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | 1,2) and Jonthan Machta ( University of Massachusetts Amherst, Brown University | | Abstract: | 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. | | Source: | arXiv, cond-mat/0408372 | | Other source: | [GID 170572] pmid15783453 | | Services: | Forum | Review | PDF | Favorites | |
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