## Abstract

We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected for a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, each job characterized by a processing time and a penalty. In the on-line version the jobs arrive one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a 1 + φ ≈ 2.618 competitive algorithm for the on-line version of the problem, where φ is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For fixed m we give improved bounds, in particular for m = 2 we give an optimal φ ≈ 1.618 competitive algorithm. For the off-line problem we present a fully polynomial approximation scheme for fixed m and an approximation algorithm which runs in time O(n log n) for arbitrary m and guarantees 2 - 1/m approximation ratio.

Original language | English |
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Title of host publication | Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 |

Publisher | Association for Computing Machinery |

Pages | 95-103 |

Number of pages | 9 |

ISBN (Electronic) | 0898713668 |

State | Published - 28 Jan 1996 |

Externally published | Yes |

Event | 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 - Atlanta, United States Duration: 28 Jan 1996 → 30 Jan 1996 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | Part F129447 |

### Conference

Conference | 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 |
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Country/Territory | United States |

City | Atlanta |

Period | 28/01/96 → 30/01/96 |

### Bibliographical note

Funding Information:‘E-mail yairb&nath. tau.ac, il. Department of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel. Research supported in part by Ben Gurion Fellowship, the Ministry of Science and Arts. tE-mail {leonardi, marchetti}Bdis .uniromai. it. Di-partimento di Informatica Sistemistica, Universita di Roma “La Sapienza”, via Salaria 113, 00198-Roma, Italia. This work was partly supported by ESPRIT BRA Alcom II under contract No.7141, and by Italian Ministry of Scientific Research Project 40% “Algoritmi, Modelli di Calcolo e Strut-ture Informative”. tErnail sgall jQearn . cvut . cz. Mathematical Institute, AV CR, Zitni 25, 115 67 Praha 1, Czech Republic; this work was done at Institute of Computer Science, Hebrew University, Jerusalem, Israel, supported in part by Golda Meir Postgraduate Fellowship.