Restructuring expression dags for efficient parallelization

TL;DR

This paper demonstrates that parallelizing the evaluation of expression dags in robust geometric computations significantly improves performance, especially when combined with effective restructuring methods.

Contribution

It introduces parallel evaluation techniques for expression dags and compares restructuring methods to optimize performance in multi-core environments.

Findings

Parallel evaluation of expression dags speeds up exact decision computations.

Restructuring methods impact the efficiency of parallel expression dag evaluation.

Parallelization yields practical performance gains in robust geometric algorithms.

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.