The parallel complexity of growth models

Machta, Jonathan; Greenlaw, Raymond

doi:10.1007/bf02179460

Cited by 17 publications

(22 citation statements)

References 26 publications

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“…Examples include the Eden model, invasion percolation, the restricted solidon-solid model [5], the Bak-Sneppen model [6] and in-ternal diffusion-limited aggregation [7] all of which can be simulated in parallel in polylogarithmic time. On the other hand, no polylog time algorithm is known for generating diffusion-limited aggregation clusters and there is evidence that only powerlaw speed-ups are possible using parallelism [8,9].…”

Section: Introductionmentioning

confidence: 99%

Parallel dynamics and computational complexity of network growth models

Machta

2005

Phys. Rev. E

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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, α 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 α = 1, where the networks become scale free. For α > 1 networks can be generated in constant time while for 0 ≤ α < 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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Section: Introductionmentioning

confidence: 99%

Parallel dynamics and computational complexity of network growth models

Machta

2005

Phys. Rev. E

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“…The scattering of the blocks over the processors leads to a spatial averaging of the load, where decreasing block sizes cause a better load balancing, but also an increasing communication overhead. [17] Especially in simulations in which the shape of the object cannot be predicted, redundant scattered decomposition is an attractive option to improve the load balance in parallel simulations [18,19].…”

Section: Figmentioning

confidence: 99%

Cellular Automata as a Mesoscopic Approach to Model and Simulate Complex Systems

Sloot

Hoekstra

2001

Computational Science — ICCS 2001

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Abstract. We discuss the cellular automata approach and its extensions, the lattice Boltzmann and multiparticle methods. The potential of these techniques is demonstrated in the case of modeling complex systems. In particular, we consider simple applications taken from various scientific domains. We discuss our distributed particle simulation of flow, based on a parallel lattice Boltzmann Method. Efficient parallel execution is possible, provided that (dynamic) load balancing techniques are applied. Next, we present a number of case studies of flow in complex geometry, i.e. flow in porous media and in static mixer reactors. The Cellular Automata ApproachA natural way to describe a physical, chemical or biological system is to propose a model of what we think is happening. During this process we try to keep only the ingredients we believe to be essential whilst still capturing the behavior we are interested in. Using an appropriate mathematical machinery, such a model can be expressed in terms a set of equations whose solution gives the desired answers on the system. The description in terms of equations is very powerful and corresponds to a rather high level of abstraction. For a long time, this methodology has been the only tractable way for scientists to address a problem.Another approach, which has been made possible by the advent of fast computers, is to stay at the level of the model and its basic components. The idea is that all the information is already contained in the model and that a computer simulation will be able to answer any possible question on the system by just running the model for some time. Thus, there is no need to use a complicated mathematical tool to obtain a high level of description. We just need to express the model in a way which is suitable to an effective computer implementation. Cellular automata constitute a paradigm in which simple models of complex phenomena can be easily formulated. In particular, cellular automata models illustrate the fact that a complex behavior emerges out of many simply interacting components through a collective effect.The degree of reality of the model depends on the level of description we expect. When we are interested in the global or macroscopic properties of a system the microscopic details of a system are often irrelevant. On the other hand, symmetries and conservation laws are usually the essential ingredients of such mesoscopic

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“…In [42] and [43] it is demonstrated that the Diffusion Limited Aggregation growth model is P-complete for which fast parallel algorithms probably do not exist, the only available option to study this type of growth processes is through explicit simulation. The basic construction of the aggregate is shown in Fig.…”

Section: A Ca Model Of the Growth Processmentioning

confidence: 99%

“…The scattering of the blocks over the processors leads to a spatial averaging of the load, where decreasing block sizes cause a better load balancing and an increasing communication overhead [57]. Especially in simulations in which the shape of the object cannot be predicted, is scattered decomposition an attractive option to improve the load balance in parallel simulations [42,43]. We have compared both decomposition strategies by computing the Load balancing efficiency:…”

Section: Parallelization Of the Ca Modelsmentioning

confidence: 99%