Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414154 | Computational Geometry | 2016 | 20 Pages |
Abstract
We consider the problem of computing the time-convex hull of a point set under the general LpLp metric in the presence of a straight-line highway in the plane. The traveling speed along the highway is assumed to be faster than that off the highway, and the shortest time-path between a distant pair may involve traveling along the highway. The time-convex hull TCH(P)TCH(P) of a point set P is the smallest set containing both P and all shortest time-paths between any two points in TCH(P)TCH(P). In this paper we give an algorithm that computes the time-convex hull under the LpLp metric in optimal O(nlogn)O(nlogn) time for a given set of n points and a real number p with 1≤p≤∞1≤p≤∞.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Bang-Sin Dai, Mong-Jen Kao, D.T. Lee,