Time Dependent Biased Random Walks
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| Title: | Time Dependent Biased Random Walks |
|---|---|
| Authors: | John Haslegrave, Thomas Sauerwald, John Sylvester |
| Contributors: | DSpace at Cambridge pro (8.1) |
| Source: | ACM Transactions on Algorithms. 18:1-30 |
| Publication Status: | Preprint |
| Publisher Information: | Association for Computing Machinery (ACM), 2022. |
| Publication Year: | 2022 |
| Subject Terms: | FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Markov chain, Probability (math.PR), G.3, G.2.2, Random walk, 0102 computer and information sciences, 01 natural sciences, PSPACE, cover time, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), F.2.2, 0101 mathematics, QA, 05C81, 60J10, 68R10, 68Q17, Markov decision process, Mathematics - Probability, Computer Science - Discrete Mathematics |
| Description: | 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. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1549-6333 1549-6325 |
| DOI: | 10.1145/3498848 |
| DOI: | 10.48550/arxiv.2006.02475 |
| DOI: | 10.17863/cam.82693 |
| Access URL: | http://arxiv.org/abs/2006.02475 http://wrap.warwick.ac.uk/160144/1/WRAP-Time-dependent-biased-random-walks-2021.pdf https://eprints.gla.ac.uk/267876/1/267876.pdf https://ora.ox.ac.uk/objects/uuid:fcd50914-f2f0-4f0b-a3ee-fc40b5c38b8b https://doi.org/10.1145/3498848 https://www.repository.cam.ac.uk/handle/1810/335261 https://doi.org/10.17863/cam.82693 https://doi.org/10.1145/3498848 |
| Rights: | arXiv Non-Exclusive Distribution rioxx All Rights Reserved URL: https://www.acm.org/publications/policies/copyright_policy#Background |
| Accession Number: | edsair.doi.dedup.....72eb70c25210b9b9bc3561ebafa5c5d4 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | 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. |
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| ISSN: | 15496333 15496325 |
| DOI: | 10.1145/3498848 |