1 research outputs found
A tight lower bound for computing the diameter of a 3D convex polytope
International audienceThe diameter of a set P of n points in âd is the maximum Euclidean distance between any two points in P. If P is the vertex set of a 3-dimensional convex polytope, and if the combinatorial structure of this polytope is given, we prove that, in the worst case, deciding whether the diameter of P is smaller than 1 requires Ω(nlogân) time in the algebraic computation tree model. It shows that the O(nlogân) time algorithm of Ramos for computing the diameter of a point set in â3 is optimal for computing the diameter of a 3-polytope. We also give a linear time reduction from Hopcroftâs problem of finding an incidence between points and lines in â2 to the diameter problem for a point set in â