### 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 language | English |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 557-566 |

Number of pages | 10 |

Publication status | Published - 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
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Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Fingerprint

### Keywords

- Algorithms
- Measurement
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Better approximation algorithms for bin covering

AU - Csirik, J.

AU - Johnson, David S.

AU - Kenyon, Claire

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Algorithms

KW - Measurement

KW - Performance

KW - Theory

KW - Verification

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M3 - Conference contribution

AN - SCOPUS:33749567103

SN - 0898714907

SP - 557

EP - 566

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ER -