Nearly Balanced Work Partitioning for Heterogeneous Algorithms

The architectural trend towards heterogeneity has pushed heterogeneous computing to the fore of parallel computing research. Heterogeneous algorithms, often carefully handcrafted, have been designed for several important problems from parallel computing such as sorting, graph algorithms, matrix computations, and the like. A majority of these algorithms follow a work partitioning approach where the input is divided into appropriate sized parts so that individual devices can process the “right” parts of the input. However, arriving at a good work partitioning is usually non-trivial and may require extensive empirical search. Such an extensive empirical search can potentially offset any gains accrued out of heterogeneous algorithms. Other recently proposed approaches too are in general inadequate.In this paper, we propose a simple and effective technique for work partitioning in the context of heterogeneous algorithms. Our technique is based on sampling and therefore can adapt to both the algorithm used and the input instance. Our technique is generic in its applicability as we will demonstrate in this paper. We validate our technique on three problems: finding the connected components of a graph (CC), multiplying two unstructured sparse matrices (spmm), and multiplying two scalefree sparse matrices. For these problems, we show that using our method, we can find the required threshold that is under 10% away from the best possible thresholds.