Optimal time-convex hull for a straight-line highway in Lp-metrics

Bang Sin Dai, Mong Jen Kao*, D. T. Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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(nlogn) time for a given set of n points and a real number p with 1 < > < >;≤.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalComputational Geometry: Theory and Applications
StatePublished - 1 Feb 2016


  • -metrics
  • Optimal convex hull
  • Time distance


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