An EPTAS for Scheduling Jobs on Uniform Processors: Using an MILP Relaxation with a Constant Number of Integral Variables

  • Authors:

  • Klaus Jansen

  • Affiliations:

  • Institut für Informatik, Universität zu Kiel, Germany

  • Venue:
  • ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
  • Year:
  • 2009

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Abstract

In this paper, we present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of $(n/\epsilon)^{O(1/\epsilon^2)}$. Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error *** of the optimum, and has running time $2^{O(1/\epsilon^2 \log(1/\epsilon)^3)} poly(n)$.