### Abstract

We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622-631; http://www.eng.tau.ac. il/∼amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215-227, 1999) to its linear programming relaxation.

Original language | English (US) |
---|---|

Pages (from-to) | 307-323 |

Number of pages | 17 |

Journal | Journal of Combinatorial Optimization |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Journal of Combinatorial Optimization*,

*4*(3), 307-323. https://doi.org/10.1023/A:1009822211065

}

*Journal of Combinatorial Optimization*, vol. 4, no. 3, pp. 307-323. https://doi.org/10.1023/A:1009822211065

**Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling.** / Berman, Piotr; Dasgupta, Bhaskar.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling

AU - Berman, Piotr

AU - Dasgupta, Bhaskar

PY - 2000/1/1

Y1 - 2000/1/1

N2 - We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622-631; http://www.eng.tau.ac. il/∼amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215-227, 1999) to its linear programming relaxation.

AB - We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622-631; http://www.eng.tau.ac. il/∼amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215-227, 1999) to its linear programming relaxation.

UR - http://www.scopus.com/inward/record.url?scp=0000332042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000332042&partnerID=8YFLogxK

U2 - 10.1023/A:1009822211065

DO - 10.1023/A:1009822211065

M3 - Article

AN - SCOPUS:0000332042

VL - 4

SP - 307

EP - 323

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 3

ER -