Supereffective slow-down of parallel computations

Brent’s scheduling principle provides a general simulation scheme when fewer processors are available than specified by the fastest parallel algorithm. Such a scheme preserves the actual number of executed operations, and when applicable, it provides a processor balancing technique that significantly reduces the work, expressed as the number of ezecutcdde operators. In this paper we discuss a new technique, called supereffective slow-down, that yields quite fast an algorithm with work significantly smaller than that of the fastest algorithm for the same problem. This technique can be viewed as a work-preserving acceleration of an existing recursive sequential algorithm for the considered problem. The presented examples include the computation of path algebras in graphs and digraphs and various computations in linear albegra. Some of the new algorithms may have practical value; for instance, we substantially improve the performance of the known parallel algorithms for triangular linear systems of equations.