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Chernoff-Hoeffding Bounds for Applications with Limited Independence
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Approximation algorithms for scheduling
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Convex quadratic and semidefinite programming relaxations in scheduling
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Introduction to Linear Optimization
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Allocating Bandwidth for Bursty Connections
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Stochastic Load Balancing and Related Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Grid 2: Blueprint for a New Computing Infrastructure
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Parallel scheduling of complex dags under uncertainty
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Improved approximations for multiprocessor scheduling under uncertainty
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Scheduling tasks with exponential duration on unrelated parallel machines
Discrete Applied Mathematics
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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 pij 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 completion time of all the jobs. 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 m log n log(n + m)/ log log(n + m))-approximation when C is a collection of disjoint chains, an O(log m log2 n)-approximation when C is a collection of directed out- or in-trees, and an O(log m log2 n log(n + m)/ log log(n + m))-approximation when C is a directed forest.