The power of two choices for random walks

Author:

Georgakopoulos Agelos,Haslegrave John,Sauerwald Thomas,Sylvester John

Abstract

AbstractWe apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number n of vertices on discrete tori and bounded degree trees, of order $${\mathcal O}(n\log \log n)$$ on bounded degree expanders, and of order $${\mathcal O}(n{(\log \log n)^2})$$ on the Erdős–Rényi random graph in a certain sparsely connected regime. We also consider the algorithmic question of computing an optimal strategy and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference34 articles.

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Multiple random walks on graphs: mixing few to cover many;Combinatorics, Probability and Computing;2023-02-15

2. The cover time of a (multiple) Markov chain with rational transition probabilities is rational;Statistics & Probability Letters;2022-08

3. Time Dependent Biased Random Walks;ACM Transactions on Algorithms;2022-03-15

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