Computational complexity of the avalanche problem on one dimensional Kadanoff sandpiles

In this paper we prove that the general avalanche problem AP is in NC, for the Kadanoff sandpile model in one dimension, answering an open problem of Formenti, Goles and Martin in 2010. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).