Acta Informatica
Stochastic Bounds on Execution Times of Parallel Programs
IEEE Transactions on Software Engineering
A heuristic of scheduling parallel tasks and its analysis
SIAM Journal on Computing
Optimal online scheduling of parallel jobs with dependencies
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Scheduling parallelizable tasks to minimize average response time
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Analyzing the expected execution times of parallel programs
SAC '97 Proceedings of the 1997 ACM symposium on Applied computing
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Stochastic Bounds for Parallel Program Execution Times with Processor Constraints
IEEE Transactions on Computers
Performance of Synchronous Parallel Algorithms with Regular Structures
IEEE Transactions on Parallel and Distributed Systems
Lower and Upper Bounds on Time for Multiprocessor Optimal Schedules
IEEE Transactions on Parallel and Distributed Systems
Stochastic bounds for parallel program execution times with processor constraints
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
Journal of Parallel and Distributed Computing - Special issue on parallel bioinspired algorithms
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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Given a set of precedence constrained parallel tasks with their processor requirements and execution times, the problem of scheduling precedence constrained parallel tasks on multicomputers with contiguous processor allocation is to find a nonpreemptive schedule of the tasks on a multicomputer such that the schedule length is minimized. This scheduling problem is substantially more difficult than other scheduling problems due to precedence constraints among tasks, the inherent difficulty of task scheduling, and processor allocation in multicomputers. We present an approximation algorithm called LLB that schedules tasks level-by-level using the largest-task-first strategy supported by the binary system partitioning scheme to handle the three difficult issues in our scheduling problem. Though algorithm LLB does not have a bounded worst-case performance ratio, we show through probabilistic analysis that LLB has a quite reasonable average-case performance ratio for typical classes of parallel computations. In particular, algorithm LLB has an average-case performance ratio less than two for large scale parallel computations that have wide task graphs (i.e., that exhibit large parallelism).