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M. Wimmer, D. Cederman, F. Versaci, J. Träff, P. Tsigas:
"Data Structures for Task-based Priority Scheduling";
Report for CoRR - Computing Research Repository; Report No. arXiv:1312.2501, 2013; 19 pages.

Many task-parallel applications can benefit from attempting to execute tasks in a specific order, as for instance indicated by priorities associated with the tasks. We present three lock-free data structures for priority scheduling with different trade-offs on scalability and ordering guarantees. First we propose a basic extension to work-stealing that provides good scalability, but cannot provide any guarantees for task-ordering in-between threads. Next, we present a centralized priority data structure based on k-fifo queues, which provides strong (but still relaxed with regard to a sequential specification) guarantees. The parameter k allows to dynamically configure the trade-off between scalability and the required ordering guarantee. Third, and finally, we combine both data structures into a hybrid, k-priority data structure, which provides scalability similar to the work-stealing based approach for larger k, while giving strong ordering guarantees for smaller k. We argue for using the hybrid data structure as the best compromise for generic, priority-based task-scheduling.
We analyze the behavior and trade-offs of our data structures in the context of a simple parallelization of Dijkstra's single-source shortest path algorithm. Our theoretical analysis and simulations show that both the centralized and the hybrid k-priority based data structures can give strong guarantees on the useful work performed by the parallel Dijkstra algorithm. We support our results with experimental evidence on an 80-core Intel Xeon system.

Task-parallel programming, priority scheduling, k-priority data structure, work-stealing, parallel single-source shortest path algorithm