article

On the Sum-of-Squares algorithm for bin packing

Authors:

David S. Johnson,

James B. Orlin,

Richard R. WeberAuthors Info & Claims

Journal of the ACM (JACM), Volume 53, Issue 1

Pages 1 - 65

https://doi.org/10.1145/1120582.1120583

Published: 01 January 2006 Publication History

Abstract

In this article we present a theoretical analysis of the online Sum-of-Squares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). We also discuss several interesting variants on SS, including a randomized O(nB log B)-time online algorithm SS* whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS* depends on a new linear-programming-based pseudopolynomial-time algorithm for solving the NP-hard problem of determining, given a discrete distribution F, just what is the growth rate for the optimal expected waste.

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Cited By

Gupta V(2024)Technical Note—Greedy Algorithm for Multiway Matching with Bounded RegretOperations Research10.1287/opre.2022.240072:3(1139-1155)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1287/opre.2022.2400
Hong YXie QWang W(2023)Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item SizesProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/36267797:3(1-46)Online publication date: 7-Dec-2023
https://dl.acm.org/doi/10.1145/3626779
Perez-Salazar SSingh MToriello A(2022)Adaptive Bin Packing with OverflowMathematics of Operations Research10.1287/moor.2021.123947:4(3317-3356)Online publication date: 1-Nov-2022
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Index Terms

On the Sum-of-Squares algorithm for bin packing
1. Theory of computation

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 53, Issue 1

January 2006

206 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1120582

Issue’s Table of Contents

Copyright © 2006 ACM.

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Publication History

Published: 01 January 2006

Published in JACM Volume 53, Issue 1

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https://dl.acm.org/doi/10.1287/moor.2021.1239
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https://doi.org/10.1287/stsy.2019.0067
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