Restructuring Expression Dags for Efficient Parallelization

Abstract

In the field of robust geometric computation it is often necessary to make exact decisions based on inexact floating-point arithmetic. One common approach is to store the computation history in an arithmetic expression dag and to re-evaluate the expression with increasing precision until an exact decision can be made. We show that exact-decisions number types based on expression dags can be evaluated faster in practice through parallelization on multiple cores. We compare the impact of several restructuring methods for the expression dag on its running time in a parallel environment.

Internal Versus External Balancing in the Evaluation of Graph-Based Number Types

“…Then obviously cost(cp(E list )) = Θ(n) and cost(cp(E bal )) = Θ(log n) (cf. [14]). So in both the serial and the parallel case, balanced graph structures are superior.…”

“…Prior to the evaluation, the expression dag can be restructured. Originally proposed by Yap [15], restructuring methods with varying degrees of invasiveness were developed [11,14]. Root-free expression trees can be restructured to reach optimal depth as shown by Brent [3].…”