9309098 Varvarigos Communication efficiency is the key to the broad success of massively parallel computation. One can see that by looking at the success stories of parallel computation, which are currently limited to applications that have small communication requirements, or use a small number of processors. In order to use massively parallel computation for a broader range of applications efficient algorithms to execute the underlying inter processor communications have to be developed. The objective of this research is to create a library of algorithms to execute a number of generic communication tasks in several multiprocessor topologies. Communication tasks and traffic patterns that arise often in applications will be examined. Emphasis will be given to finding easily implementable communication algorithms to execute these tasks in optimal or near-optimal time. These algorithms can be called as communication primitives by the programmer of the compiler of a multiprocessor computer in the same way that subroutines implementing standard functions are called from a library of functions in a conventional computer. ***