Abstract
The sandpile model, introduced by Bak, Tang and Wiesenfeld in 1987, is the standard example for a dynamic model showing Self-Organized Criticality (SOC). Also, it has many nice algebraic properties; for example, there is a set of configurations which is a group with a certain naturally defined addition.
We look at elements c, d of this group and try to find out how long it takes to naively compute the sum c ⊕ d. While we can easily give an upper bound, it is harder to find a lower bound. We prove some facts about the number of topplings (elementary operations) that have to be performed during the addition of two elements of the group and give a heuristic for quickly finding local minima.
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References
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© 2008 Springer-Verlag Berlin Heidelberg
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Schulz, M. (2008). On the Addition of Recurrent Configurations of the Sandpile-Model. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_30
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DOI: https://doi.org/10.1007/978-3-540-79992-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
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