Euclidean shortest paths in simple cube curves at a glance

Abstract

This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by ε > 0, and in time complexity k(ε) · σ(n), where k(ε) is the length difference between the path used for initialization and the minimum-length path, divided by ε. A run-time diagram also illustrates this linear-time behavior of the implemented ESP algorithm. © Springer-Verlag Berlin Heidelberg 2007.