Dr Mustazee Rahman mustazee.rahman@durham.ac.uk
Associate Professor
We show that the largest density of factor of i.i.d. independent sets in the d -regular tree is asymptotically at most ( log d ) / d as d → ∞ . This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random d -regular graphs have the same asymptotic density. In contrast, the density of the largest independent sets in these graphs is asymptotically 2 ( log d ) / d . We prove analogous results for Poisson–Galton–Watson trees, which yield bounds for local algorithms on sparse Erdős–Rényi graphs.
Rahman, M., & Virág, B. (2017). Local algorithms for independent sets are half-optimal. Annals of Probability, 45(3), 1543-1577. https://doi.org/10.1214/16-aop1094
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 11, 2016 |
Online Publication Date | May 15, 2017 |
Publication Date | 2017 |
Deposit Date | Sep 25, 2019 |
Publicly Available Date | Oct 4, 2021 |
Journal | Annals of Probability |
Print ISSN | 0091-1798 |
Publisher | Institute of Mathematical Statistics |
Peer Reviewed | Peer Reviewed |
Volume | 45 |
Issue | 3 |
Pages | 1543-1577 |
DOI | https://doi.org/10.1214/16-aop1094 |
Published Journal Article
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Copyright © 2017 Institute of Mathematical Statistics
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