Approximate Euclidean Shortest Paths in 3-Space-Reference-Cited by-同舟云学术

Approximate Euclidean Shortest Paths in 3-Space

Published:1997-08 Issue:04 Volume:07 Page:271-295
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

Choi Joonsoo¹,Sellen Juergen¹,Yap Chee-Keng¹

Affiliation:

1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, New York

Abstract

Papadimitriou's approximation approach to the Euclidean shortest path (ESP) in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. However, there are several gaps in the original description. Besides giving a complete treatment in the framework of bit complexity, we also improve on his subdivision method. Among the tools needed are root-separation bounds and nontrivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195997000181

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