Balancing expression dags for more efficient lazy adaptive evaluation

TL;DR

This paper proposes balancing arithmetic expression dags to improve the efficiency of lazy adaptive evaluation, predicting and confirming asymptotic performance gains.

Contribution

It introduces a restructuring method for expression dags by balancing operations, enhancing evaluation efficiency in geometric computing.

Findings

Asymptotic improvement in running time predicted and experimentally confirmed.

Balancing expression dags can lead to more efficient lazy evaluation.

Discussion of potential pitfalls due to changes in evaluation order.

Abstract

Arithmetic expression dags are widely applied in robust geometric computing. In this paper we restructure expression dags by balancing consecutive additions or multiplications. We predict an asymptotic improvement in running time and experimentally confirm the theoretical results. Finally, we discuss some pitfalls of the approach resulting from changes in evaluation order.