Better approximation algorithms for bin covering

J. Csirik, David S. Johnson, Claire Kenyon

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

37 Citations (Scopus)

Abstract

Bin covering takes as input a list of items with sizes in (0, 1) and places them into bins of unit demand so as to maximize the number of bins whose demand is satisfied. This is in a sense a dual problem to the classical one-dimensional bin packing problem, but has for many years lagged behind the latter in terms of the guality of the best approximation algorithms. We design algorithms for this problem that close the gap, both in terms of worst- and average-case results. We present (1) the first asymptotic approximation scheme for the offline version, (2) algorithms that have bounded worst-case behavior for instances with discrete item sizes and expected behavior that is asymptotically optimal for all discrete "perfect-packing distributions" (ones for which optimal packings have sublinear expected waste), and (3) a learning algorithm that has asymptotically optimal expected behavior for all discrete distributions. The algorithms of (2) and (3) are based on the recently-developed online Sum-of-Squares algorithm for bin packing. We also present experimental analysis comparing the algorithms of (2) and suggesting that one of them, the Sum-of-Squares-with-Threshold algorithm, performs guite well even for discrete distributions that do not have the perfect-packing property.

Original languageEnglish
Title of host publicationProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Pages557-566
Number of pages10
Publication statusPublished - 2001
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: Apr 30 2001May 1 2001

Other

Other2001 Operating Section Proceedings, American Gas Association
CountryUnited States
CityDallas, TX
Period4/30/015/1/01

Fingerprint

Bins
Approximation algorithms
Approximation Algorithms
Covering
Packing
Discrete Distributions
Sum of squares
Asymptotically Optimal
Bin Packing Problem
Bin Packing
Algorithm Design
Asymptotic Approximation
Dual Problem
Experimental Analysis
Approximation Scheme
Best Approximation
Learning Algorithm
Learning algorithms
Maximise
Unit

Keywords

  • Algorithms
  • Measurement
  • Performance
  • Theory
  • Verification

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Csirik, J., Johnson, D. S., & Kenyon, C. (2001). Better approximation algorithms for bin covering. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 557-566)

Better approximation algorithms for bin covering. / Csirik, J.; Johnson, David S.; Kenyon, Claire.

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. p. 557-566.

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

Csirik, J, Johnson, DS & Kenyon, C 2001, Better approximation algorithms for bin covering. in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 557-566, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.
Csirik J, Johnson DS, Kenyon C. Better approximation algorithms for bin covering. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. p. 557-566
Csirik, J. ; Johnson, David S. ; Kenyon, Claire. / Better approximation algorithms for bin covering. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2001. pp. 557-566
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