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The rotor-router model, also known as the Propp machine, is a deterministic process analogous to a random walk on a graph. Instead of distributing tokens to randomly chosen neighbors, the rotor-router deterministically serves the neighbors in a fixed order. This paper is concerned with a generalized model, functional-router model. While the rotor-router is… (More)

Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates de-terministic random walks, which is a deterministic process analogous to a random walk. While there are several progresses on the analysis of the vertex-wise discrepancy (i.e., L ∞ discrepancy), little is known about the total variation discrepancy (i.e., L 1… (More)

The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk, nothing is known about the cover time of deterministic random walks emulating general transition probabilities. This paper… (More)

Pull voting is a classic method to reach consensus among n vertices with differing opinions in a distributed network: each vertex at each step takes on the opinion of a random neighbour. This method, however, suffers from two drawbacks. Even if there are only two opposing opinions, the time taken for a single opinion to emerge can be slow and the final… (More)

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