### Abstract

We consider an online job scheduling problem on a single machine with precedence constraints under uncertainty. In this problem, for each trial t = 1,..., T, the player chooses a total order (permutation) of n fixed jobs satisfying some prefixed precedence constraints. Then, the adversary determines the processing time for each job, 9 and the player incurs as loss the sum of the processing time and the waiting time. The goal of the player is to perform as well as the best fixed total order of jobs in hindsight. We formulate the problem as an online linear optimization problem over the permutahedron (the convex hull of permutation vectors) with specific linear constraints, in which the underlying decision space is written with exponentially many linear constraints. We propose a polynomial time online linear optimization algorithm; it predicts almost as well as the state-of-the-art offline approximation algorithms do in hindsight.

Original language | English |
---|---|

Title of host publication | Algorithmic Learning Theory - 26th International Conference, ALT 2015 |

Editors | Claudio Gentile, Sandra Zilles, Kamalika Chaudhuri |

Publisher | Springer Verlag |

Pages | 332-346 |

Number of pages | 15 |

ISBN (Print) | 9783319244853 |

DOIs | |

Publication status | Published - 2015 |

Event | 26th International Conference on Algorithmic Learning Theory, ALT 2015 - Banff, Canada Duration: Oct 4 2015 → Oct 6 2015 |

### Publication series

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

Volume | 9355 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Conference on Algorithmic Learning Theory, ALT 2015 |
---|---|

Country | Canada |

City | Banff |

Period | 10/4/15 → 10/6/15 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Online linear optimization for job scheduling under precedence constraints'. Together they form a unique fingerprint.

## Cite this

*Algorithmic Learning Theory - 26th International Conference, ALT 2015*(pp. 332-346). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9355). Springer Verlag. https://doi.org/10.1007/978-3-319-24486-0_22