Balanced Allocations: Caching and Packing, Twinning and Thinning

Los, Dimitrios, Sauerwald, Thomas and Sylvester, John ORCID: 0000-0002-6543-2934 (2022) Balanced Allocations: Caching and Packing, Twinning and Thinning. In: Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics, pp. 1847-1874. ISBN 9781611977073

Access the full-text of this item by clicking on the Open Access link.

Official URL: http://dx.doi.org/10.1137/1.9781611977073.74

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:	Book Section
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	14 Mar 2023 10:31
Last Modified:	14 Oct 2023 08:37
DOI:	10.1137/1.9781611977073.74
Open Access URL:	https://doi.org/10.1137/1.9781611977073.74
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3168975