Fast Divide-and-Conquer Algorithms for Preemptive Scheduling Problems with Controllable Processing Times – A Polymatroid Optimization Approach

  • Natalia V. Shakhlevich
  • Akiyoshi Shioura
  • Vitaly A. Strusevich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

Abstract

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in \( \O({\rm T}_{\rm feas}(n) \times\log n)\) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Natalia V. Shakhlevich
    • 1
  • Akiyoshi Shioura
    • 2
  • Vitaly A. Strusevich
    • 3
  1. 1.School of ComputingUniversity of LeedsLeedsU.K.
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.Department of Mathematical SciencesUniversity of GreenwichLondonU.K.

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