Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric
Computational Geometry
2021-07-01 v1
Abstract
We consider the time-convex hull problem in the presence of two orthogonal highways H. In this problem, the travelling speed on the highway is faster than off the highway, and the time-convex hull of a point set P is the closure of P with respect to the inclusion of shortest time-paths. In this paper, we provide the algorithm for constructing the time-convex hull with two orthogonal highways. We reach the optimal result of O(n log n) time for arbitrary highway speed in the L1-metric. For the L2-metric with infinite highway speed, we hit the goal of O(n log n) time as well.
Keywords
Cite
@article{arxiv.2106.15885,
title = {Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric},
author = {Jyun-Yu Chen and Po-Hsuan Chen},
journal= {arXiv preprint arXiv:2106.15885},
year = {2021}
}