Average-Case Analysis of Isospeed Scalability of Parallel Computations on Multiprocessors

We investigate the average-case speed and scalability of parallel algorithms executing on multiprocessors. Our performance metrics are average-speed and isospeed scalability. By modeling parallel algorithms on multiprocessors using task precedence graphs, we are mainly interested in the effects of synchronization overhead and load imbalance on the performance of parallel computations. Thus, we focus on the structures of parallel computations, whose inherent sequential parts are limitations to high performance. For several typical classes of task graphs, including iterative computations, search trees, partitioning algorithms, and diamond dags, we derive the growth rate of the number of tasks as well as isospeed scalability in keeping constant average-speed.