Polynomial bound for a chip firing game on graphs
SIAM Journal on Discrete Mathematics
Sandpile transience on the grid is polynomially bounded
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The Computational Complexity of One-Dimensional Sandpiles
Theory of Computing Systems
On the Complexity of Sandpile Prediction Problems
Electronic Notes in Theoretical Computer Science (ENTCS)
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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In this work, we study The Abelian Sandpile Model from the point of view of computational complexity. We begin by studying the length distribution of sandpile avalanches triggered by the addition of two critical configurations: we prove that those avalanches are long on average, their length is bounded below by a constant fraction of the length of the longest critical avalanche which is, in most of the cases, superlinear. At the end of the paper we take the point of view of computational complexity, we analyze the algorithmic hardness of the problem consisting in computing the addition of two critical configurations, we prove that this problem is P complete, and we prove that most algorithmic problems related to The Abelian Sandpile Model are NC reducible to it.