### Abstract

In this paper we consider a basic scheduling problem called the busy time scheduling problem - given n jobs, with release times r_{j} , deadlines dj and processing times p_{j}and m machines, where each machine can run up to g jobs concurrently, our goal is to find a schedule to minimize the sum of the “on” times for the machines. We develop the first correct constant factor online competitive algorithm for the case when g is unbounded, and give a O(log P) approximation for general g, where P is the ratio of maximum to minimum processing time. When g is bounded, all prior busy time approximation algorithms use an unbounded number of machines; note it is NP-hard just to test feasibility on fixed m machines. For this problem we give both offline and online (requiring “lookahead”) algorithms, which are O(1) competitive in busy time and O(log P) competitive in number of machines used.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings |

Editors | Faith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack |

Publisher | Springer Verlag |

Pages | 521-532 |

Number of pages | 12 |

ISBN (Print) | 9783319621265 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada Duration: Jul 31 2017 → Aug 2 2017 |

### 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 | 10389 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th International Symposium on Algorithms and Data Structures, WADS 2017 |
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Country | Canada |

City | St. John’s |

Period | 7/31/17 → 8/2/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings*(pp. 521-532). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10389 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-62127-2_44