Algorithms for stable sorting to minimize communications in networks of workstations and their implementations in BSP

We introduce a novel approach to produce BSP (Bulk Synchronous Programming model) programs and we show their efficiency by implementing the stable sorting problem on clusters of PC. Experimental results on PCs based on Ethernet and Myrinet cards are compared with implementations on an SGI 2000. The algorithms presented in the paper are either developed under the theoretical framework of the Regular Sampling technique which guarantees good load balancing properties or are inspired by the technique in order to decrease the sequential work of each processor comparing to the Regular Sampling technique but impose no (theoretical) bound on load balancing. The main sequential block of code used in the algorithms for local sorting are derivatives of Shellsort (which is stable) and a new code based on Quicksort (which is not stable) plus a property on real numbers that is used for stable sorting under the framework of BSR (Broadcast with Selective Reduction)