Time dependent biased random walks

Haslegrave, J., Sauerwald, T. and Sylvester, J. (2022) Time dependent biased random walks. ACM Transactions on Algorithms, 18(2), pp. 1-30. (doi: 10.1145/3498848)

[img] Text
267876.pdf - Accepted Version

584kB

Abstract

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 p to p 1-ε ; 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 PSPACE -complete.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Sylvester, Dr John
Authors: Haslegrave, J., Sauerwald, T., and Sylvester, J.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:ACM Transactions on Algorithms
Publisher:Association for Computing Machinery (ACM)
ISSN:1549-6325
ISSN (Online):1549-6333
Copyright Holders:Copyright © 2022 Association for Computing Machinery
First Published:First published in ACM Transactions on Algorithms 18(2):1-30
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

University Staff: Request a correction | Enlighten Editors: Update this record