# 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} }

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…

## 17 Citations

Theoretical aspects of scheduling coupled-tasks in the presence of compatibility graph

- Computer ScienceAlgorithmic Oper. Res.
- 2011

A generalization of the coupled-task sche-duling problem introduced by Shapiro, where considered tasks are subject to incompatibility constraints depicted by an undirected graph is presented, and a new polynomial-time approximation algorithm result is given which completes previous works.

Scheduling stretched coupled-tasks with compatibilities constraints : model, complexity and approximation results for some class of graphs

- Computer Science
- 2014

This work tackles the makespan minimization coupled-tasks problem in presence of compatibility constraints and proposes some efficient polynomial-time approximation algorithms according to difference parameters of the scheduling problem.

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

- Computer ScienceRAIRO Oper. Res.
- 2016

This work considers the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology and designs some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters.

Identical coupled task scheduling problem: the finite case

- Business
- 2011

Coupled tasks belong to the class of multi-operation tasks, where two consecutive operations are separated by a certain time interval of fixed duration. The objective is to schedule the tasks on one…

Identical coupled task scheduling: polynomial complexity of the cyclic case

- BusinessJ. Sched.
- 2015

The purpose of the article is to solve this open problem in the cyclic case, for which it is proved the polynomial complexity, and to solve the identical coupled task problem.

A Binary Search Method for the General Coupled Task Scheduling Problem

- Business, Computer ScienceSSRN Electronic Journal
- 2019

This work studies the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NP-hard and proposes a binary search heuristic algorithm for the problem.

A binary search algorithm for the general coupled task scheduling problem

- Business, Computer Science4OR
- 2021

This work studies the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NP-hard and proposes a binary search heuristic algorithm for the problem.

Coupled-Tasks in Presence of Bipartite Compatibilities Graphs

- Computer ScienceISCO
- 2014

This work tackles the makespan minimization coupled-tasks problem in presence of incompatibility constraints and designs efficient polynomial-time approximation algorithms according to different parameters of the scheduling problem.

Coupled Task Scheduling With Exact Delays: Literature Review and Models

- BusinessEur. J. Oper. Res.
- 2020

Abstract The coupled task scheduling problem concerns scheduling a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to…

Approximation algorithm for constrained coupled-tasks scheduling problem

- Computer Science2014 International Conference on Control, Decision and Information Technologies (CoDIT)
- 2014

This work tackles the makespan minimization coupled-tasks problem in presence of compatibility constraints and proposes some complexity results according to several parameters and designs an efficient polynomial-time approximation algorithm.

## 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.

An exact algorithm for scheduling identical coupled tasks

- Computer ScienceMath. 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 ScienceJ. 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 Science2009 International Conference on Computers & Industrial Engineering
- 2009

A note on the complexity of scheduling coupled tasks on a single processor

- BusinessJ. 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…

Scheduling coupled tasks

- Business
- 1980

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 ScienceJACM
- 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 ScienceTheor. 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, MathematicsTheor. Comput. Sci.
- 1991