Complexity of scheduling parallel task systems
SIAM Journal on Discrete Mathematics
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Scheduling on hierarchical clusters using malleable tasks
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Approximation Algorithms for Scheduling Malleable Tasks under Precedence Constraints
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Scheduling malleable tasks with precedence constraints
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Critical Path and Area Based Scheduling of Parallel Task Graphs on Heterogeneous Platforms
ICPADS '06 Proceedings of the 12th International Conference on Parallel and Distributed Systems - Volume 1
Tightness results for malleable task scheduling algorithms
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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The model of moldable task (MT) was introduced some years ago and has been proven to be an efficient way for implementing parallel applications. It considers a target application at a larger level of granularity than in other models (typically corresponding to numerical routines) where the tasks can themselves be executed in parallel on any number of processors. Clusters of SMPs (symmetric Multi-Processors) are a cost effective alternative to parallel supercomputers. Such hierarchical clusters are parallel systems made from m identical SMPs composed each by k identical processors. These architectures are more and more popular, however designing efficient software that take full advantage of such systems remains difficult. This work describes approximation algorithms for scheduling a set of tree precedence constrained moldable tasks for the minimization of the parallel execution time, with a scheme which is first used for two multi-processors and several bi-processors and then extended to the general case of any number of multi-processors. The best known approximations of competitive ratios for trees in the homogeneous case is 2.62, and although the hierarchical problem is harder our results are close as we obtain a ratio of 3.41 for two multi-processors, 3.73 for several bi-processors and 5.61 for the general case of several SMPs with a large number of processors. To our knowledge, this is the first work on precedence constrained moldable tasks on hierarchical platforms.