Approximation Algorithms for Multiprocessor Scheduling under Uncertainty

Motivated by applications in grid computing and projects 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 in [21] 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...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Guolong Lin, Rajmohan Rajaraman
• Keywords: CORR 2007, Directed Acyclic Graph, Education, Machine, Multiprocessor