Inverse Avalanches On Abelian Sandpiles
  A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be optimal in the sense that it requires the minimum amount of computation among methods of the same kind. The method is also conceptually nice because avalanche and inverse avalanche are placed in the same footing. 
H. F. Chau (School of Natural Sciences, Institute for Advanced Study,   Olden Lane, Princeton, NJ 08540 and Department of Ph...