Euclidean Shortest Paths in Simple Cube Curves at a Glance.

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 $\kappa(\varepsilon) \cdot {\cal O}(n)$, where κ(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. [ABSTRACT FROM AUTHOR]