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arXiv · 2106.15885

Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric

Jyun-Yu Chen·Po-Hsuan Chen
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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.

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Jyun-Yu Chen, Po-Hsuan Chen. 2021-06-30. Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric. https://arxiv.org/abs/2106.15885

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