On the Sum-of-Squares algorithm for bin packing

J. 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 sub-linear 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 publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
PublisherACM
Pages208-217
Number of pages10
Publication statusPublished - 2000
Event32nd Annual ACM Symposium on Theory of Computing - Portland, OR, USA
Duration: May 21 2000May 23 2000

Other

Other32nd Annual ACM Symposium on Theory of Computing
CityPortland, OR, USA
Period5/21/005/23/00

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Bins
Linear programming
Computational complexity

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 Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 208-217). ACM.

On the Sum-of-Squares algorithm for bin packing. / Csirik, J.; Johnson, David S.; Kenyon, Claire; Orlin, James B.; Shor, Peter W.; Weber, Richard R.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, 2000. p. 208-217.

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

Csirik, J, Johnson, DS, Kenyon, C, Orlin, JB, Shor, PW & Weber, RR 2000, On the Sum-of-Squares algorithm for bin packing. in Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, pp. 208-217, 32nd Annual ACM Symposium on Theory of Computing, Portland, OR, USA, 5/21/00.
Csirik J, Johnson DS, Kenyon C, Orlin JB, Shor PW, Weber RR. On the Sum-of-Squares algorithm for bin packing. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM. 2000. p. 208-217
Csirik, J. ; Johnson, David S. ; Kenyon, Claire ; Orlin, James B. ; Shor, Peter W. ; Weber, Richard R. / On the Sum-of-Squares algorithm for bin packing. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, 2000. pp. 208-217
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