Balanced Allocations: Caching and Packing, Twinning and Thinning

Los, D., Sauerwald, T. and Sylvester, J. (2022) Balanced Allocations: Caching and Packing, Twinning and Thinning. In: 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 09-12 Jan 2022, pp. 1847-1874. ISBN 9781611977073 (doi: 10.1137/1.9781611977073.74)

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Abstract

We consider the sequential allocation of m balls (jobs) into n bins (servers) by allowing each ball to choose from some bins sampled uniformly at random. The goal is to maintain a small gap between the maximum load and the average load. In this paper, we present a general framework that allows us to analyze various allocation processes that slightly prefer allocating into underloaded, as opposed to overloaded bins. Our analysis covers several natural instances of processes, including: • The Caching process (a.k.a. memory protocol) as studied by Mitzenmacher, Prabhakar and Shah (2002). • The Packing process: At each round we only take one bin sample. If the load is below some threshold (e.g., the average load), then we place as many balls until the threshold is reached; otherwise, we place only one ball. • The Twinning process: At each round, we only take one bin sample. If the load is below some threshold, then we place two balls; otherwise, we place only one ball. • The Thinning process as recently studied by Feldheim and Gurel-Gurevich (2021). As we demonstrate, using an interplay between several potential functions our general framework implies for all these processes a gap of O(log n) for any number of balls m ≥ n.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Sylvester, Dr John
Authors: Los, D., Sauerwald, T., and Sylvester, J.
College/School:College of Science and Engineering > School of Computing Science
ISBN:9781611977073
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
305944Multilayer Algorithmics to Leverage Graph StructureKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/T004878/1M&S - Statistics