COMMUNICATION BALANCING IN THE PARALLEL GÖTTFERT ALGORITHM

Abstract

Parallel implementations in computer algebra often require careful designs tailored towards irregular data structures and patterns of computation that are largely unpredictable. In this context, we re-visit the BSP Göttfert algorithm of [1] whose communication patterns suffer from greatly varying degrees within the intermediary univariate polynomial outputs, leading to unpredictable communication load imbalance. We show that this problem can be rectified through the use of two-phase broadcast. We demonstrate the effects of our improvement using analysis within the BSP model. We conduct a series of experimental comparative runs for factoring input polynomials with degrees ranging from 8000 to 400000, over a number of processors reaching up to 16. Our communication balancing results in an improvement in most of the test cases, more so whenever stark deviation in intermediary polynomial degrees is observed.