arXiv subjects

Yam Ki Cheung

Publications and source records attributed to Yam Ki Cheung.

2 recordsLinked to original sources

arXiv2010

Fréchet Distance Problems in Weighted Regions

We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1+epsilon)-factor approximation of the Fréchet distance between two polygonal curves. We also consider the Fréchet distance between two polygonal curves among polyhedral obstacles in R^3 and present a (1+epsilon)-factor approximation algorithm.

cs.CG↗

arXiv2010

Approximate Point-to-Face Shortest Paths in R^3

We address the point-to-face approximate shortest path problem in R: Given a set of polyhedral obstacles with a total of n vertices, a source point s, an obstacle face f, and a real positive parameter epsilon, compute a path from s to f that avoids the interior of the obstacles and has length at most (1+epsilon) times the length of the shortest obstacle avoiding path from s to f. We present three approximation algorithms that take by extending three well-known "point-to-point" shortest path algorithms.

cs.CG↗