Theory of Computing Systems

, Volume 47, Issue 4, pp 856–877 | Cite as

Approximation Algorithms for Multiprocessor Scheduling under Uncertainty

  • Guolong Lin
  • Rajmohan RajaramanEmail author


Motivated by applications in grid computing and project management, we study multiprocessor scheduling in scenarios where there is uncertainty in the successful execution of jobs when assigned to processors. We consider the problem of multiprocessor scheduling under uncertainty, in which we are given n unit-time jobs and m machines, a directed acyclic graph C giving the dependencies among the jobs, and for every job j and machine i, the probability p ij of the successful completion of job j when scheduled on machine i in any given particular step. The goal of the problem is to find a schedule that minimizes the expected makespan, that is, the expected time at which all of the jobs are completed.

The problem of multiprocessor scheduling under uncertainty was introduced by Malewicz and was shown to be NP-hard even when all the jobs are independent. In this paper, we present polynomial-time approximation algorithms for the problem, for special cases of the dag C. We obtain an O(log n)-approximation for the case of independent jobs, an O(log mlog nlog (n+m)/log log (n+m))-approximation when C is a collection of disjoint chains, an O(log mlog 2 n)-approximation when C is a collection of directed out- or in-trees, and an O(log mlog 2 nlog (n+m)/log log (n+m))-approximation when C is a directed forest.


Approximation algorithms Multiprocessor scheduling 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Akamai TechnologiesCambridgeUSA
  2. 2.College of Computer and Information ScienceNortheastern UniversityBostonUSA

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