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...

• Type: Journal
• Year: 2010
• Where: ACRI
• Authors: Carolina Mejía, J. Andrés Montoya
• Keywords: Abelian Sandpile Model, ACRI 2010, Artificial Intelligence, Avalanches, Critical Avalanches