### Abstract

We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bin-stretching problem that guarantee a stretching factor of 5/3 for any number m of bins. We then combine the two algorithms and design an algorithm whose stretching factor is 1:625 for any m. The analysis for the performance of this algorithm is tight. The best lower bound for any algorithm is 4/3 for any m≥2. We note that the bin-stretching problem is also equivalent to the classical scheduling (load balancing) problem in which the value of the makespan (maximum load) is known in advance.

Original language | English (US) |
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Title of host publication | Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings |

Publisher | Springer Verlag |

Pages | 71-81 |

Number of pages | 11 |

Volume | 1518 |

ISBN (Print) | 354065142X, 9783540651420 |

DOIs | |

State | Published - 1998 |

Event | 2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998 - Barcelona, Spain Duration: Oct 8 1998 → Oct 10 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1518 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998 |
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Country | Spain |

City | Barcelona |

Period | 10/8/98 → 10/10/98 |

### Fingerprint

### Keywords

- Approximation algorithms
- Bin-packing
- Bin-stretching
- Load balancing
- On-line algorithms
- Scheduling

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings*(Vol. 1518, pp. 71-81). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1518). Springer Verlag. https://doi.org/10.1007/3-540-49543-6_7

**On-line bin-stretching.** / Azar, Yossi; Regev, Oded.

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

*Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings.*vol. 1518, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1518, Springer Verlag, pp. 71-81, 2nd International Workshop on Randomization and Approximation Techniques in Computer Science, Random 1998, Barcelona, Spain, 10/8/98. https://doi.org/10.1007/3-540-49543-6_7

}

TY - GEN

T1 - On-line bin-stretching

AU - Azar, Yossi

AU - Regev, Oded

PY - 1998

Y1 - 1998

N2 - We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bin-stretching problem that guarantee a stretching factor of 5/3 for any number m of bins. We then combine the two algorithms and design an algorithm whose stretching factor is 1:625 for any m. The analysis for the performance of this algorithm is tight. The best lower bound for any algorithm is 4/3 for any m≥2. We note that the bin-stretching problem is also equivalent to the classical scheduling (load balancing) problem in which the value of the makespan (maximum load) is known in advance.

AB - We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bin-stretching problem that guarantee a stretching factor of 5/3 for any number m of bins. We then combine the two algorithms and design an algorithm whose stretching factor is 1:625 for any m. The analysis for the performance of this algorithm is tight. The best lower bound for any algorithm is 4/3 for any m≥2. We note that the bin-stretching problem is also equivalent to the classical scheduling (load balancing) problem in which the value of the makespan (maximum load) is known in advance.

KW - Approximation algorithms

KW - Bin-packing

KW - Bin-stretching

KW - Load balancing

KW - On-line algorithms

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=77955834557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955834557&partnerID=8YFLogxK

U2 - 10.1007/3-540-49543-6_7

DO - 10.1007/3-540-49543-6_7

M3 - Conference contribution

SN - 354065142X

SN - 9783540651420

VL - 1518

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 71

EP - 81

BT - Randomization and Approximation Techniques in Computer Science - 2nd International Workshop, RANDOM 1998, Proceedings

PB - Springer Verlag

ER -