Inverse Avalanches On Abelian Sandpiles

TL;DR

This paper introduces an efficient and conceptually elegant method for computing inverse avalanches in Abelian sandpiles, aligning the inverse process with the forward avalanche in a minimal computational framework.

Contribution

It presents the inverse particle addition operator, a novel, optimal method for inverse avalanche computation in Abelian sandpiles, unifying the forward and inverse processes.

Findings

Method is computationally efficient

Requires minimal computation among similar methods

Unifies avalanche and inverse avalanche processes

Abstract

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.