The Cover Time of Deterministic Random Walks for General Transition Probabilities

TL;DR

This paper establishes the first upper bound on the cover time of deterministic random walks that emulate general transition probabilities, extending understanding beyond simple models like rotor-router.

Contribution

It introduces an upper bound for the cover time of the SRT-router model with multiple tokens, applicable to general transition probabilities, including irrational numbers.

Findings

First upper bound on cover time for general transition probabilities

Improves existing bounds for rotor-router model in some cases

Extends deterministic walk analysis beyond simple random walk emulation

Abstract

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 is concerned with the 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.