1. On the parameterized complexity of interval scheduling with eligible machine sets.
- Author
-
Hermelin, Danny, Itzhaki, Yuval, Molter, Hendrik, and Shabtay, Dvir
- Subjects
- *
OPERATIONS research , *SCHEDULING , *MACHINERY , *COMPUTER scheduling - 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 p max. 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 p max = O (1) and present an FPT -algorithm with for the combined parameter m + p max. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF