Theory of Computing Systems

, Volume 39, Issue 1, pp 121–136 | Cite as

The Expected Competitive Ratio for Weighted Completion Time Scheduling

  • Alexander Souza
  • Angelika Steger


A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a diffuse adversary chooses the distribution Fj of the random processing time Pj from a certain class of distributions F j. The scheduler is given the expectation μj = E[Pj], but the actual duration is not known in advance. A positive weight wj is associated with each job j and all jobs are ready for execution at time zero. The scheduler determines a list of the jobs, which is then scheduled in a non-preemptive manner. The objective is to minimise the total weighted completion time ∑j wj Cj. The performance of an algorithm is measured with respect to the expected competitive ratio maxF ∈ F E[∑j wj Cj/OPT], where Cj denotes the completion time of job j and OPT the offline optimum value. We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions. This class includes, among others, the exponential distribution. As a special case, we consider the popular rule weighted shortest expected processing time first (WSEPT) in which jobs are processed according to the non-decreasing μj/wj ratio. We show that it achieves E[WSEPT/OPT] ≤ 3 – 1/m for exponential distributed processing times.


Processing Time Completion Time Schedule Algorithm Parallel Machine Competitive Ratio 
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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institute of Theoretical Computer Science, ETH Zurich, Universitatstr. 6, CH-8092 ZurichSwitzerland

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