Journal of Scheduling

, Volume 14, Issue 5, pp 501–509 | Cite as

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

  • G. Simonin
  • B. Darties
  • R. Giroudeau
  • J.-C. König
Article

Abstract

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 minimization of the schedule length, we show that finding a solution to our problem amounts to solving a graph problem, which in itself is close to the minimum-disjoint-path cover (min-DCP) problem. We design a \((\frac{3a+2b}{2a+2b})\)-approximation, where a and b (the processing time of the two sub-tasks) are two input data such as a>b>0, and that leads to a ratio between \(\frac {3}{2}\) and \(\frac{5}{4}\). Using a polynomial-time algorithm developed for some class of graph of min-DCP, we show that the ratio decreases to \(\frac{1+\sqrt{3}}{2}\approx 1.37\).

Keywords

Coupled-tasks Complexity Compatibility graph Polynomial-time approximation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • G. Simonin
    • 1
  • B. Darties
    • 2
  • R. Giroudeau
    • 1
  • J.-C. König
    • 1
  1. 1.LIRMM UMR 5506Montpellier Cedex 5France
  2. 2.LE2I UMR 5158DijonFrance

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