Better approximation algorithms for bin covering

Janos Csirik, David S. Johnson, Claire Kenyon

Research output: Conference contribution

39 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 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages557-566
Number of pages10
Publication statusPublished - dec. 1 2001
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: ápr. 30 2001máj. 1 2001

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

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

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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  • Cite this

    Csirik, J., Johnson, D. S., & Kenyon, C. (2001). Better approximation algorithms for bin covering. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 557-566). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).