Hyperbolic 0-1 programming and query optimization in information retrieval
Mathematical Programming: Series A and B
Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan
Journal of the ACM (JACM)
Introduction to Algorithms
Parallel scheduling of complex dags under uncertainty
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Approximation algorithms for multiprocessor scheduling under uncertainty
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Scheduling Algorithms
NP-complete scheduling problems
Journal of Computer and System Sciences
On complexity of unconstrained hyperbolic 0-1 programming problems
Operations Research Letters
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This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among m tasks that n workers are scheduled to execute. The question is to find a schedule @S such that if tasks are assigned to workers according to @S, the expected time needed to execute all the tasks is minimized. The time needed to execute task t by worker w is a random variable expressed by a negative exponential distribution with parameter @l"w"t and each task can be executed by more than one worker at a time. In this paper, we will prove that the problem in its general form is NP-hard, but when the DAG width is constant, we will show that the optimum schedules can be found in polynomial time.