# Isomorphic coupled-task scheduling problem with compatibility constraints on a single processor

@article{Simonin2011IsomorphicCS,
title={Isomorphic coupled-task scheduling problem with compatibility constraints on a single processor},
author={Gilles Simonin and Beno{\^i}t Darties and Rodolphe Giroudeau and Jean-Claude K{\"o}nig},
journal={Journal of Scheduling},
year={2011},
volume={14},
pages={501-509}
}
• Published 10 August 2009
• Computer Science
• Journal of Scheduling
The problem presented in this paper is a generalization of the usual coupled-tasks scheduling problem in presence of compatibility constraints. The reason behind this study is the data acquisition problem for a submarine torpedo. We investigate a particular configuration for coupled tasks (any task is divided into two sub-tasks separated by an idle time), in which the idle time of a coupled task is equal to the sum of durations of its two sub-tasks. We prove $\mathcal{NP}$-completeness of the…
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## References

SHOWING 1-10 OF 27 REFERENCES
Extended Matching Problem for a Coupled-Tasks Scheduling Problem
• Computer Science
• 2009
This paper introduces a scheduling problem with coupled-tasks in presence of a compatibility graph on a single processor, and proposes a polynomial-time algorithm which consists in minimizing the number of non-covered vertices, by covering vertices with edges or paths of length two in the compatibility graph.
On the Complexity of Coupled-task Scheduling
• Computer Science
Discret. Appl. Math.
• 1997
An exact algorithm for scheduling identical coupled tasks
• Computer Science
Math. Methods Oper. Res.
• 2004
An exact algorithm for the coupled task problem to schedule n jobs on one machine where each job consists of two subtasks with required delay time between them with time complexity O(nr2L) where holds.
Scheduling of coupled tasks with unit processing times
• Computer Science
J. Sched.
• 2010
It is proved that the general problem of coupled tasks scheduling on a single processor, under the assumptions that all processing times are equal to 1, the gap has exact integer length L and the precedence constraints are strict, is NP-hard in the strong sense.
Complexity and approximation for scheduling problem for a torpedo
• Computer Science
2009 International Conference on Computers & Industrial Engineering
• 2009
A note on the complexity of scheduling coupled tasks on a single processor
J. Braz. Comput. Soc.
• 2001
This paper considers a problem of coupled task scheduling on one processor, where all processing times are equal to 1, the gap has exact length h, precedence constraints are strict and the criterion
This article discusses several candidate techniques for schedule determination, and these are evaluated in a specific radar scheduling application.
Advances on the Hamiltonian Completion Problem
• Mathematics, Computer Science
JACM
• 1975
Linear algorithms are presented for solving the Hamiltonian completion problem for several classes of graphs, in particular for trees and unicyclic graphs.
A time-optimal solution for the path cover problem on cographs
• Mathematics, Computer Science
Theor. Comput. Sci.
• 2003
We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved time- and work-optimally for
Optimal Covering of Cacti by Vertex-Disjoint Paths
• Computer Science, Mathematics
Theor. Comput. Sci.
• 1991