On the sum-of-squares algorithm for bin packing

Janos Csirik, David S. Johnson, Claire Kenyon, James B. Orlin, Peter W. Shor, Richard R. Weber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)

Abstract

In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], 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). In addition, we present a randomized O(nB log B)-time on-line algorithm SS*, based on SS, whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS* also 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. An off-line randomized variant SS** performs well in a worst-case sense: For any list L of integer-sized items to be packed into bins of a fixed size B, the expected number of bins used by SS** is at most OPT(L) + √OPT(L).

Original languageEnglish
Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Pages208-217
Number of pages10
DOIs
Publication statusPublished - Dec 1 2000
Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
Duration: May 21 2000May 23 2000

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
CountryUnited States
CityPortland, OR
Period5/21/005/23/00

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ASJC Scopus subject areas

  • Software

Cite this

Csirik, J., Johnson, D. S., Kenyon, C., Orlin, J. B., Shor, P. W., & Weber, R. R. (2000). On the sum-of-squares algorithm for bin packing. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000 (pp. 208-217). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/335305.335331