Journal of Scheduling

, Volume 12, Issue 2, pp 199–224

Scheduling with conflicts: online and offline algorithms

  • Guy Even
  • Magnús M. Halldórsson
  • Lotem Kaplan
  • Dana Ron
Article

DOI: 10.1007/s10951-008-0089-1

Cite this article as:
Even, G., Halldórsson, M.M., Kaplan, L. et al. J Sched (2009) 12: 199. doi:10.1007/s10951-008-0089-1

Abstract

We consider the following problem of scheduling with conflicts (swc): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs.

Our first main positive result is an exact algorithm for two machines and job sizes in {1,2}. For jobs sizes in {1,2,3}, we can obtain a \(\frac{4}{3}\) -approximation, which improves on the \(\frac{3}{2}\) -approximation that was previously known for this case. Our main negative result is that for jobs sizes in {1,2,3,4}, the problem is APX-hard.

Our second contribution is the initiation of the study of an online model for swc, where we present the first results in this model. Specifically, we prove a lower bound of \(2-\frac{1}{m}\) on the competitive ratio of any deterministic online algorithm for m machines and unit jobs, and an upper bound of 2 when the algorithm is not restricted computationally. For three machines we can show that an efficient greedy algorithm achieves this bound. For two machines we present a more complex algorithm that achieves a competitive ratio of \(2-\frac{1}{7}\) when the number of jobs is known in advance to the algorithm.

Keywords

Scheduling with conflicts Mutual exclusion scheduling Approximation algorithms Online algorithms 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Guy Even
    • 1
  • Magnús M. Halldórsson
    • 2
  • Lotem Kaplan
    • 1
  • Dana Ron
    • 1
  1. 1.School of Electrical EngineeringTel-Aviv Univ.Tel-AvivIsrael
  2. 2.Dept. of Computer Science, Faculty of EngineeringUniversity of IcelandReykjavíkIceland

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