## Abstract

In online interval scheduling, the input is an online sequence of intervals, and the goal is to accept a maximum number of non-overlapping intervals. In the more general disjoint path allocation problem, the input is a sequence of requests, each involving a pair of vertices of a known graph, and the goal is to accept a maximum number of requests forming edge-disjoint paths between accepted pairs. These problems have been studied under extreme settings without information about the input or with error-free advice. We study an intermediate setting with a potentially erroneous prediction that specifies the set of intervals/requests forming the input sequence. For both problems, we provide tight upper and lower bounds on the competitive ratios of online algorithms as a function of the prediction error. For disjoint path allocation, our results rule out the possibility of obtaining a better competitive ratio than that of a simple algorithm that fully trusts predictions, whereas, for interval scheduling, we develop a superior algorithm. We also present asymptotically tight trade-offs between consistency (competitive ratio with error-free predictions) and robustness (competitive ratio with adversarial predictions) of interval scheduling algorithms. Finally, we provide experimental results on real-world scheduling workloads that confirm our theoretical analysis.

Original language | English |
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Title of host publication | Algorithms and Data Structures : Proceedings of 18th International Symposium |

Editors | Pat Morin, Subhash Suri |

Publisher | Springer |

Publication date | 2023 |

Pages | 193-207 |

ISBN (Print) | 9783031389054 |

DOIs | |

Publication status | Published - 2023 |

Event | 18th International Algorithms and Data Structures Symposium - Montreal, QC, Canada Duration: 31. Jul 2023 → 2. Aug 2023 |

### Conference

Conference | 18th International Algorithms and Data Structures Symposium |
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Country/Territory | Canada |

City | Montreal, QC |

Period | 31/07/2023 → 02/08/2023 |

## Keywords

- Algorithms with prediction
- Competitive analysis
- Disjoint paths
- Online interval scheduling