Fixed Order Scheduling with Deadlines
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910944416759808 |
|---|---|
| author | Berger, Andre Rouhani, Arman Schröder, Marc |
| author_facet | Berger, Andre Rouhani, Arman Schröder, Marc |
| contents | This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the number of machines while ensuring deadlines are met and the fixed order is maintained. We show that the first-fit algorithm solves the problem optimally with unit processing times and is a 2-approximation in the following four cases: (1) the order aligns with non-increasing slacks, (2) the order aligns with non-decreasing slacks, (3) the order aligns with non-increasing deadlines, and (4) the optimal solution uses at most 3 machines. For the general problem we provide an $O(\log n)$-approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10760 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed Order Scheduling with Deadlines Berger, Andre Rouhani, Arman Schröder, Marc Data Structures and Algorithms This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the number of machines while ensuring deadlines are met and the fixed order is maintained. We show that the first-fit algorithm solves the problem optimally with unit processing times and is a 2-approximation in the following four cases: (1) the order aligns with non-increasing slacks, (2) the order aligns with non-decreasing slacks, (3) the order aligns with non-increasing deadlines, and (4) the optimal solution uses at most 3 machines. For the general problem we provide an $O(\log n)$-approximation. |
| title | Fixed Order Scheduling with Deadlines |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2412.10760 |