Design and evaluation of update schemes to optimize asynchronous Cellular Automata with random or cyclic orders

Abstract

Cellular Automata (CA) remain actively used to model phenomena as diverse as crowd evacuation, urban planning, or tumors. In their simplest form, CA use a synchronous approach such that cells are updated all together. This perfectly synchronous update has been criticized for lack of realism, as it produces outcomes that may not be obtained with less synchronization. Consequently, CA may use an asynchronous update to overcome some of these artifacts. While numerous works have shown how to scale CA models by parallelizing their synchronous updates, a paucity of research has explored the asynchronous case. We present and empirically evaluate algorithms for efficient parallel executions of two types of asynchronous updates: random order and cyclic order. Our algorithms select random orderings that suit parallel execution and are therefore approximate in nature. Our results suggest that they can effectively leverage parallelism while keeping results well aligned with the sequential baseline implementation.