Optimal Time-Convex Hull under the L p Metrics
نویسندگان
چکیده
We consider the problem of computing the time-convex hull of a point set under the general Lp 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 Lp metric in optimal O(n log n) time for a given set of n points and a real number p with 1 ≤ p ≤ ∞.
منابع مشابه
7. Acknowledgments 8. References 6. Concluding Remarks
Optimal algorithms for computing the minimum distance between two finite planar sets, " Proc. A fast algorithm for the planar convex hull problem, " internal manuscript, [25] B. K. Bhattacharya and G. T. Toussaint. " A time-and-storage efficient implementation of an optimal planar convex hull algorithm, " Divide and conquer for linear expected time, " Inform. A linear algorithm for finding the ...
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