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Special Issue on Cellular Automata Theory and ApplicationsNo Access

HOW FAR IS IT TO THE NEXT RECURRENT CONFIGURATION? AN NP-COMPLETE PROBLEM IN THE SANDPILE MODEL

    We take a look at transient configurations of the Abelian Sandpile Model (ASM). If we add enough grains on the "right" sites to this configuration we get a recurrent configuration of the ASM. In this paper we show that it is NP-complete to decide for a transient configuration c on a grid of size m × m and a natural number k if it is possible to add k grains of sand to c such that we get a recurrent configuration. We show this by reducing the problem of deciding whether a given planar cubic graph of size n ∈ Θ(m) has a vertex cover, which is NP-complete, to this problem.

    References