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To improve the performance of scientific applications with parallel loops, dynamic loop scheduling methods have been proposed. Such methods address performance degradations due to load imbalance caused by predictable phenomena like nonuniform data distribution or algorithmic variance, and unpredictable phenomena such as data access latency or operating system interference. In particular, methods such as factoring, weighted factoring, adaptive weighted factoring, and adaptive factoring have been developed based on a probabilistic analysis of parallel loop iterates with variable running times. These methods have been successfully implemented in a number of applications such as: N-Body and Monte Carlo simulations, computational fluid dynamics, and radar signal processing.The focus of this paper is on adaptive weighted factoring (AWF), a method that was designed for scheduling parallel loops in time-stepping scientific applications. The main contribution of the paper is to relax the time-stepping requirement, a modification that allows the AWF to be used in any application with a parallel loop. The modification further allows the AWF to adapt to load imbalance that may occur during loop execution. Results of experiments to compare the performance of the modified AWF with the performance of the other loop scheduling methods in the context of three nontrivial applications reveal that the performance of the modified method is

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Although N-body simulation algorithms are amenable to parallelization, performance gains from execution on parallel machines are di cult to obtain due to load imbalances caused by irregular distributions of bodies. In general, there is a tension between balancing processor loads and maintaining locality, as the dynamic re-assignment o f w ork necessitates access to remote data. Fractiling is a dynamic scheduling scheme that simultaneously balances processor loads and maintains locality b y exploiting the self-similarity properties of fractals. Fractiling is based on a probabilistic analysis, and thus, accommodates load imbalances caused by predictable phenomena, such as irregular data, and unpredictable phenomena, such as data-access latencies. In experiments on a KSR1, performance of N-body simulation codes were improved by a s m uch as 53% by fractiling. Performance improvements were obtained on uniform and nonuniform distributions of bodies, underscoring the need for a scheduling scheme that accommodates system induced variance. As the fractiling scheme is orthogonal to the N-body algorithm, we could use simple codes that discretize space into equal-size subrectangles (2-d) or subcubes (3-d) as the base algorithms.