Towards efficient BSP implementations of BSR programs for some computational geometry problems

In this paper we present our investigations to implement some computational geometry problems (point in a polygon, intersection problem, convex hull) under the framework of BSR (Broadcasting with Selective Reduction) model of parallel computing, then under the framework of BSP (Bulk Synchronous Parallel Model) programs. BSR is a (theoretical) model with the capabilities of PRAM models augmented with a broadcast mechanism. BSR offers concise notations that facilitates the specification part. BSP is suitable for concrete implementation because it also characterizes prediction in terms of a small set of machine parameters. So, instead of implementing in hardware the primitives of the BSR model we consider practical rules to translate BSR constructions into BSP ones. We also validate the discussion by translating BSR programs into BSP programs. We run them both on Silicon Graphics Origin2000 and on a Bi-Pentium 300 MHz. The results encourage us to develop a computational geometry problems starting from a BSR specification that is automatically translated into efficient BSP implementations. The results are pretty good and demonstrate that BSR can be used as specification language which is implemented in software by BSP primitives