Random walks are frequently used in randomized algorithms. We study a derandomized variant of a random walk on graphs called the rotor-router model. In this model, instead of distributing tokens randomly, each vertex serves its neighbors in a fixed ...

The rotor-router model is a deterministic process analogous to a simple random walk on a graph, and the discrepancy of token configurations between the rotor-router model and its corresponding random walk has been investigated in some contexts. Motivated by ...

Let $G$ be a connected, loopless multigraph. The sandpile group of $G$ is a finite abelian group associated to $G$ whose order is equal to the number of spanning trees in $G$. Holroyd et al. used a dynamical process on graphs called rotor-routing to define ...

We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process. Starting from an ...

What is the property that a randomized algorithm really requires for randomness? This note reviews some randomized algorithms which the author has been concerned with, having been motivated by the above question.

Jim Propp's rotor–router model is a deterministic analog of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order.

Cooper and Spencer (Comb Probab Comput 15 (2006) 815–822) show a remarkable ...