Time Dependent Biased Random Walks



Haslegrave, John, Sauerwald, Thomas and Sylvester, John ORCID: 0000-0002-6543-2934
(2022) Time Dependent Biased Random Walks. ACM TRANSACTIONS ON ALGORITHMS, 18 (2). pp. 1-30.

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Abstract

<jats:p> We study the biased random walk where at each step of a random walk a “controller” can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC’1992]; we extend their work to the time dependent setting and consider cover times of this walk. We obtain new bounds on the cover and hitting times. Azar et al. conjectured that the controller can increase the stationary probability of a vertex from <jats:italic>p</jats:italic> to <jats:italic>p</jats:italic> <jats:sup>1-ε</jats:sup> ; while this conjecture is not true in full generality, we propose a best-possible amended version of this conjecture and confirm it for a broad class of graphs. We also consider the problem of computing an optimal strategy for the controller to minimise the cover time and show that for directed graphs determining the cover time is <jats:monospace>PSPACE</jats:monospace> -complete. </jats:p>

Item Type: Article
Uncontrolled Keywords: Random walk, cover time, Markov chain, Markov decision process, PSPACE
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 14 Mar 2023 10:32
Last Modified: 14 Mar 2023 10:32
DOI: 10.1145/3498848
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3168973