The Complexity of Three-Dimensional Critical Avalanches

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The Complexity of Three-Dimensional Critical Avalanches
In this work we study the complexity of the three-dimensional sandpile avalanches triggered by the addition of two critical configurations. We prove that the algorithmic problem consisting in predicting the evolution of three dimensional critical avalanches is the hardness core of the three-dimensional Abelian Sandpile Model. On the other hand we prove that three-dimensional critical avalanches are superlinear long on average. It suggests that the prediction problem is superlinear-hard on average. Can we quickly predict the evolution of an avalanche if we are given a full description of the initial conditions? The Abelian Sandpile Model has been used to simulate dissipative dynamical process such as forest fires, earth quakes, extinction events, and (off course) avalanches [2]. Can we quickly predict sandpile avalanches? There is some previous work concerning the computational complexity of prediction problems related to The Abelian Sandpile Model (see for example [3], and [4]). Mos...
Carolina Mejía, J. Andrés Montoya
Added 12 Jan 2011
Updated 12 Jan 2011
Type Journal
Year 2010
Where ACRI
Authors Carolina Mejía, J. Andrés Montoya
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