### Abstract

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(T_{feas}(n)× log n) time by using our divide-and-conquer technique, where n is the number of jobs and O(T _{feas}(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

Original language | English |
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Title of host publication | Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings |

Pages | 756-767 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2008 Dec 24 |

Event | 16th Annual European Symposium on Algorithms, ESA 2008 - Karlsruhe, Germany Duration: 2008 Sep 15 → 2008 Sep 17 |

### 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 | 5193 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Annual European Symposium on Algorithms, ESA 2008 |
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Country | Germany |

City | Karlsruhe |

Period | 08/9/15 → 08/9/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings*(pp. 756-767). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5193 LNCS). https://doi.org/10.1007/978-3-540-87744-8-63