On the parameterized complexity of interval scheduling with eligible machine sets

Danny Hermelin; Yuval Itzhaki; Hendrik Molter; Dvir Shabtay

doi:10.1016/j.jcss.2024.103533

On the parameterized complexity of interval scheduling with eligible machine sets

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, Dvir Shabtay

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	103533
Journal	Journal of Computer and System Sciences
Volume	144
DOIs	https://doi.org/10.1016/j.jcss.2024.103533
State	Published - 1 Sep 2024

Keywords

Eligible machine sets
Fixed-parameter tractability
Interval scheduling
Just-in-time scheduling
W[1]-hardness

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2024.103533

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title = "On the parameterized complexity of interval scheduling with eligible machine sets",

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.",

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author = "Danny Hermelin and Yuval Itzhaki and Hendrik Molter and Dvir Shabtay",

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AU - Itzhaki, Yuval

AU - Molter, Hendrik

AU - Shabtay, Dvir

PY - 2024/9/1

Y1 - 2024/9/1

N2 - 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.

AB - 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.

KW - Eligible machine sets

KW - Fixed-parameter tractability

KW - Interval scheduling

KW - Just-in-time scheduling

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On the parameterized complexity of interval scheduling with eligible machine sets

Abstract

Keywords

ASJC Scopus subject areas

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