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On the Complexity of Minimizing the Total Calibration Cost

  • Eric Angel
  • Evripidis Bampis
  • Vincent ChauEmail author
  • Vassilis Zissimopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

Bender et al. (SPAA 2013) proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Since calibrations have non negligible cost, it is important to study policies minimizing the calibration cost while performing all the necessary tests. We focus on the single-machine setting and we study the complexity status of different variants of the problem. First, we extend the model by considering that the jobs have arbitrary processing times and that the preemption of jobs is allowed. For this case, we propose an optimal polynomial time algorithm. Then, we study the case where there is many types of calibrations with different lengths and costs. We prove that the problem becomes NP-hard for arbitrary processing times even when the preemption of the jobs is allowed. Finally, we focus on the case of unit-time jobs and we show that a more general problem, where the recalibration of the machine is not instantaneous, can be solved in polynomial time.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Eric Angel
    • 1
  • Evripidis Bampis
    • 2
  • Vincent Chau
    • 3
    Email author
  • Vassilis Zissimopoulos
    • 4
  1. 1.IBISCUniversité d’Évry Val d’EssonneÉvryFrance
  2. 2.Sorbonne Universités, UPMC Univ. Paris 06, UMR 7606, LIP6ParisFrance
  3. 3.Shenzhen Institutes of Advanced TechnologyAcademy of SciencesShenzhenChina
  4. 4.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensAthensGreece

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