Approximating a coupled-task scheduling problem in the presence of compatibility graph and additional tasks

Simonin, Gilles; Giroudeau, Rodolphe; König, Jean-Claude

doi:10.1504/ijps.2013.059680

Cited by 4 publications

(7 citation statements)

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“…Thus a maximum matching in the compatibility graph leads to an optimal solution for the 3-unit CTS Problem, see [24] for more details. In the same paper, the authors prove that for L ≥ 5 the L-unit CTS Problem is N P-complete (the hardness for L = 4 is given in [23]), and so is the L-unit CTS Problem for L ≥ 4 and also the CTS Problem. Thus, we assume that L ≥ 4 for the rest of the paper.…”

Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 98%

“…The absence of compatibility constraints corresponds to the case of a complete compatibility graph Gc. The model in which the complete compatibility graph is relaxed has been studied in the framework of classic complexity and approximation, mainly in [23] and [24]. Remark that for L = 2, the L-unit CTS Problem is trivial, as there are no idle times and any permutation of the tasks is an optimal scheduling.…”

Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 99%

“…Thus, we assume that L ≥ 4 for the rest of the paper. Concerning approximation algorithms, it is shown in [23] that the 4-unit CTS Problem admits a polynomial 13 12 -approximation algorithm. Whereas, in [24] a 4+L 4 -approximation algorithm is given for the general Lunit CTS Problem.…”

Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 99%

“…Indeed it is possible that some tasks could not interleave with some other tasks. It occurs when several tasks need to use a resource, different from the processor, available sequentially (this model is proposed in [23] and motivated by data acquisition and processing in a mono-processor torpedo used for underwater exploration). In order to represent these constraints, a compatibility graph Gc = (A, Ec) is introduced, where the set of Gc-vertices is the set A of coupled-tasks and [A i , A j ] ∈ Ec if, and only if, the two coupled-tasks A i and A j can be interleaved.…”

Section: Introductionmentioning

confidence: 99%

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Parameterized complexity of a coupled-task scheduling problem

Bessy

Giroudeau

2018

J Sched

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In this article, we investigate the parameterized complexity of coupled-task scheduling in the presence of compatibility constraint given by a compatibility graph. In this model, each task contains two sub-tasks delayed by an idle time, and a subtask of a task can be performed during the idle time of another one if, and only if, the two tasks are compatible. We consider a parameterized version of the scheduling problem: is there a schedule in which at least k coupled-tasks possess a completion time before a fixed due date? It is known that this problem is N P-complete ([23] and [24]), and we prove that it is fixed-parameter tractable (FPT) if the total duration time of each task is bounded by a constant, whereas the problem becomes W[1]-hard if it is not the case. We also show that in the former case the problem does not admit a polynomial kernel under some standard complexity assumptions. Moreover, we obtain also an FPT algorithm when the problem is parameterized by the size of a vertex cover of the compatibility graph.

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Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 98%

Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 99%

Section: Coupled-tasks Scheduling Problem (Cts Problem)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parameterized complexity of a coupled-task scheduling problem

Bessy

Giroudeau

2018

J Sched

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“…They considered equal delays for all the jobs and showed that the problem is NP-hard when L 3. They presented an approximation algorithm with a ratio of L+6 Simonin et al (2013) studied the problem under the conditions of with and without"triangles connectivity" in the compatibility graph. They showed that the problem is NP-hard under both conditions, and presented a 10 9 ( 13 12 )-approximation algorithm for the existence (lack) of triangles.…”

Section: Restrictions On the Job Sequencementioning

confidence: 99%

Coupled Task Scheduling With Exact Delays: Literature Review and Models

2018

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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 optimize a performance criterion. While research on the problem dates back to the 1980s, interests in the computational complexity of variants of the problem and solution methodologies have been evolving in the past few years. This motivates us to present an up-to-date and comprehensive literature review on the topic. Aiming to provide a complete road map for future research on the coupled task scheduling problem, we discuss all the relevant studies and potential research opportunities. In addition, we propose several sets of benchmark instances for the problem in various settings and provide a detailed evaluation of all the available models with a view to facilitating future research on the solution methods.

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