ITR: A New Computational Paradigm: Robustness as a Resource

New York University, New York NY

Investigators

Abstract

The problem of numerical robustness and geometric consistency is well known in many areas of computational science. The issue is that inexact computer arith- metic leads to incorrect and inconsistent geometric conclusions (for example, is a point inside or outside a triangle). While computers are getting faster, software is not getting more robust. Indeed, the trend is towards more nonrobustness. We propose a new computational paradigm to reverse this trend. Robustness is often seen as an all-or-nothing proposition. Our new paradigm consists in viewing robustness as a computational resource, to be traded off against other resources such as speed. Each program defines a certain robustness-speed trade-off curve; we want to be able to run the program at any point along this curve. This proposal will develop the technology to make this capability effcient and easily accessible to all programmers. As a result, any programmer can produce nearly ordinary C/C++ code which can be run robustly. The implications of this paradigm are wide ranging, and will bring the fruits of robustness research into mainstream computing. We propose to (1) conduct basic research to support this new computing paradigm, (2) to create the technology and software tools to achieve this paradigm, and (3) to explore the applications of fast and usually robust algorithms in algo- rithm design. For (1), we will focus on effciency issues such as novel root bounds, incremental computation, guaranteed absolute precision for elementary functions. For (2), we expect to significantly extend the power, efficiency and usability of our Core Library and include capabilities such as symbolic perturbation. Finally an example of (3) concerns the general problem of checking of geometric structures and their applications in new efficient geometric algorithms. We propose to apply our robustness techniques and software to two significant applications in which nonrobustness problems are well-known: * Mesh Generation: we will construct the first fully robust mesh generator which will be deployed in a major ow solver system, Cart3d. * Geometric Modeling: we will build a robust geometric modeler which will be the first such system that is precision-sensitive. This proposal involves international collaboration with Professor Mehlhorn's Algorithms and Complexity Group at the Max-Planck Institute of Computer Sci- ence in Germany. Our domestic collaborator are Michael Aftosmis from NASA Ames Research Center (on mesh generation) and Shankar Krishnan from AT&T Research Laboratories (on geometric modeling).