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 |
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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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