The cover time of deterministic random walks for general transition probabilities

Abstract

A 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 is concerned with the shortest remaining time (SRT)-router model with multiple tokens, which is a deterministic process coping with general transition probabilities possibly containing irrational numbers. For the model, we give an upper bound of the cover time, which is the first result on the cover time of deterministic random walks for general transition probabilities. Our upper bound also improves the existing bounds for the rotor-router model in some cases.