Approximation algorithms for scheduling with reservations

  • Authors:

  • Florian Diedrich;Klaus Jansen;Fanny Pascual;Denis Trystram

  • Affiliations:

  • Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany;Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany;LIG, Grenoble University, Montbonnot Saint-Martin, France;LIG, Grenoble University, Montbonnot Saint-Martin, France

  • Venue:
  • HiPC'07 Proceedings of the 14th international conference on High performance computing
  • Year:
  • 2007

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Abstract

We study the problem of scheduling n independent jobs on a system of m identical parallel machines in the presence of reservations. This constraint is practically important; for various reasons, some machines are not available during specified time intervals. The objective is to minimize the makespan. This problem is inapproximable in the general case unless P = NP which motivates the study of suitable restrictions. We use an approach based on algorithms for multiple subset sum problems; our technique yields a polynomial time approximation scheme (PTAS) which is best possible in the sense that the problem does not admit an FPTAS unless P = NP. The PTAS presented here is the first one for the problem under consideration; so far, not even for special cases approximation schemes have been proposed. We also derive a low cost algorithm with a constant approximation ratio and discuss additional FPTASes for special cases and complexity results.