Abstract
We provide new parameterized complexity results for INTERVAL SCHEDULING ON ELIGIBLE MACHINES. In this problem, a set of n jobs is given to be processed non-preemptively on a set of m machines. Each job has a processing time, a deadline, a weight, and a set of eligible machines that can process it. The goal is to find a maximum weight subset of jobs that can each be processed on one of its eligible machines such that it completes exactly at its deadline. We focus on two parameters: The number m of machines, and the largest processing time pmax. Our main contribution is showing W[1]-hardness when parameterized by m. This answers Open Problem 8 of Mnich and van Bevern's list of 15 open problems in parameterized complexity of scheduling problems [Computers & Operations Research, 2018]. Furthermore, we show NP-hardness even when pmax=O(1) and present an FPT-algorithm with for the combined parameter m+pmax.
| Original language | American English |
|---|---|
| Article number | 103533 |
| Journal | Journal of Computer and System Sciences |
| Volume | 144 |
| DOIs | |
| State | Published - 1 Sep 2024 |
Keywords
- Eligible machine sets
- Fixed-parameter tractability
- Interval scheduling
- Just-in-time scheduling
- W[1]-hardness
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- General Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics
Fingerprint
Dive into the research topics of 'On the parameterized complexity of interval scheduling with eligible machine sets'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver