A Partitioning-Independent Paradigm for Nested Data Parallelism

A generalization of the data parallel model has been proposed by Blelloch which permits the nesting of data parallel operators to specify parallel computation across nested and irregular data structures. In this paper we consider the costs of supporting the general model of nested data parallelism, analyzing the requirements such a model places upon an underlying model of execution. We propose a new multi-node execution model which meets the needs of the paradigm and is additionally generic in the partitioning of data aggregates within the system. The basis for our execution model is an abstract machine based upon elementary notions of nodal multi-threading. We demonstrate the utility of our proposal by providing a full definition for a simple nestable one-dimensional data parallel operator. We discuss the applicability of our design to existing multi-processor machines, illustrating performance statistics gathered from a prototype system we have constructed on the Thinking Machines CM-5.