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Self-stabilizing balls and bins in batches: The power of leaky bins
journal contribution
posted on 2018-01-24, 11:38 authored by Petra Berenbrink, Tom Friedetzky, Peter Kling, Frederik Mallmann-Trenn, Lars NagelLars Nagel, Chris WastellA fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed among n bins (servers). In a seminal work, Azar et al. [4] proposed the sequential strategy Greedy[d] for n = m. Each ball queries the load of d random bins and is allocated to a least loaded of them. Azar et al. showed that d = 2 yields an exponential improvement compared to d = 1. Berenbrink et al. [7] extended this to m n, showing that for d = 2 the maximal load difference is independent of m (in contrast to the d = 1 case). We propose a new variant of an infinite balls-into-bins process. In each round an expected number of λn new balls arrive and are distributed (in parallel) to the bins, and each non-empty bin deletes one of its balls. This setting models a set of servers processing incoming requests, where clients can query a server’s current load but receive no information about parallel requests. We study the Greedy[d] distribution scheme in this setting and show a strong self-stabilizing property: for any arrival rate λ = λ(n) < 1, the system load is time-invariant. Moreover, for any (even super-exponential) round t, the maximum system load is (w.h.p.) O 1 1−λ· log n 1−λ for d = 1 and O log n 1−λ for d = 2. In particular, Greedy[2] has an exponentially smaller system load for high arrival rates.
Funding
Petra Berenbrink is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Peter Kling is partly supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Pacific Institute for the Mathematical Sciences (PIMS). Lars Nagel is supported by the German Ministry of Education and Research under Grant 01IH13004. Christopher Wastell is supported by EPSRC.
History
School
- Science
Department
- Computer Science
Published in
AlgorithmicaVolume
80Pages
3673 - 3703Citation
BERENBRINK, P. ... et al, 2018. Self-stabilizing balls and bins in batches: The power of leaky bins. Algorithmica, 80 (12), pp.3673–3703.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2018-01-24Publication date
2018-02-15Notes
This is a post-peer-review, pre-copyedit version of an article published in Algorithmica. The final authenticated version is available online at: https://doi.org/10.1007/s00453-018-0411-z.ISSN
0178-4617eISSN
1432-0541Publisher version
Language
- en