Abstract
This interdisciplinary research examines several algorithms from statistical physics that generate random fractals. The algorithms are studied using parallel complexity theory. Decision problems based on diffusion limited aggregation and a number of widely used algorithms for equilibrating the Ising model are proved P-complete. This is in contrast to Mandelbrot percolation that is shown to be in (non-uniform) AC 0. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have recently been studied using complexity theory. The results may serve as a guide to simulation physics.
This research partially supported by National Science Foundation grant CCR-9209184 and a Spanish Fellowship for Scientific and Technical Investigations 1996. Part of this research was conducted while Ray was on sabbatical at UPC in Barcelona and the department's hospitality is greatly appreciated.
This research was partially funded by the National Science Foundation Grant DMR-9311580.
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© 1996 Springer-Verlag Berlin Heidelberg
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Greenlaw, R., Machta, J. (1996). The parallel complexity of randomized fractals. In: Ferreira, A., Rolim, J., Saad, Y., Yang, T. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1996. Lecture Notes in Computer Science, vol 1117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030126
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DOI: https://doi.org/10.1007/BFb0030126
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