Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Santa Claus Schedules Jobs on Unrelated Machines

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time p_{ij} if processed on machine i. More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form p_{ij} in {p_j, \infty}. This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than 1.5 which is also the best known lower bound for the general version. Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor 33/17 + \epsilon \approx 1.9412 + \epsilon, where \epsilon > 0 is an arbitrarily small constant. The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as configuration LP, that was previously successfully used for the related Santa Claus problem. Similar to the strongest analysis for that problem our proof is based on a local search algorithm that will eventually find a schedule of the mentioned approximation guarantee, but is not known to converge in polynomial time.

      Related collections

      Most cited references 10

      • Record: found
      • Abstract: not found
      • Article: not found

      Approximation algorithms for scheduling unrelated parallel machines

        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        The Santa Claus problem

          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          Exact and Approximate Algorithms for Scheduling Nonidentical Processors

            Bookmark

            Author and article information

            Journal
            04 November 2010
            2011-03-21
            1011.1168

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            22 pages, 1 figure; corrected typos and changed some notation
            cs.DS

            Comments

            Comment on this article