Abstract
We consider the problem of computing the time-convex hull of a point set under the general L p 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) of a point set P is the smallest set containing both P and all shortest time-paths between any two points in TCH(P). In this paper we give an algorithm that computes the time-convex hull under the L p metric in optimal \(\mathcal{O}(n\log n)\) time for a given set of n points and a real number p with 1 ≤ p ≤ ∞.
This work was supported in part by National Science Council (NSC), Taiwan, under grants NSC-101-2221-E-005-026 and NSC-101-2221-E-005-019.
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Dai, BS., Kao, MJ., Lee, D.T. (2013). Optimal Time-Convex Hull under the L p Metrics. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_24
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DOI: https://doi.org/10.1007/978-3-642-40104-6_24
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