Job Scheduling Using Successive Linear Programming Approximations of a Sparse Model

  • Stephane Chretien
  • Jean-Marc Nicod
  • Laurent Philippe
  • Veronika Rehn-Sonigo
  • Lamiel Toch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7484)


In this paper we tackle the well-known problem of scheduling a collection of parallel jobs on a set of processors either in a cluster or in a multiprocessor computer. For the makespan objective, i.e., the completion time of the last job, this problem has been shown to be NP-Hard and several heuristics have already been proposed to minimize the execution time. We introduce a novel approach based on successive linear programming (LP) approximations of a sparse model. The idea is to relax an integer linear program and use ℓ p norm-based operators to force the solver to find almost-integer solutions that can be assimilated to an integer solution. We consider the case where jobs are either rigid or moldable. A rigid parallel job is performed with a predefined number of processors while a moldable job can define the number of processors that it is using just before it starts its execution. We compare the scheduling approach with the classic Largest Task First list based algorithm and we show that our approach provides good results for small instances of the problem. The contributions of this paper are both the integration of mathematical methods in the scheduling world and the design of a promising approach which gives good results for scheduling problems with less than a hundred processors.


Schedule Problem Completion Time Integer Linear Program Compress Sensing Virtual Machine Migration 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stephane Chretien
    • 1
  • Jean-Marc Nicod
    • 2
  • Laurent Philippe
    • 2
  • Veronika Rehn-Sonigo
    • 2
  • Lamiel Toch
    • 2
  1. 1.Department of MathematicsUniversité de Franche-ComtéBesançonFrance
  2. 2.FEMTO-ST Institute, UMR CNRS / UFC / ENSMM / UTBMBesançonFrance

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