We present simple output-sensitive algorithms that construct the convex hull of a set ofn points in two or three dimensions in worst-case optimal O (n logh) time andO (n) space, whereh denotes the number of vertices.Expand

We consider two problems: given a collection of n fat objects in a fixed dimension, (1) (packing) find the maximum subcollection of pairwise disjoint objects, and (2) (piercing)find the minimum point set that intersects every object.Expand

In the first part of the paper, we reexamine the all-pairs shortest path (APSP) problem and present a new algorithm with running time $O(n^3log^3\log n/\log^2n)$, which improves all known algorithms for general real-weighted dense graphs.Expand

We present the first optimal algorithm to compute the maximumTukey depth (also known as <i>location or halfspace depth</i>) for a non-degenerate point set in the plane.Expand

This paper describes further refinements of Sharir and Eppstein’s deterministic and randomized algorithms for the planar Euclidean two-center problem.Expand

We speed up previous (1 + e)-factor approximation algorithms for a number of geometric optimization problems in fixed dimensions by improving the dependence of the "constants" in terms of e.Expand

We present a simple algorithm in two dimensions that runs in O((n+k2)log n) expected time; this is faster than earlier algorithms by Everett, Robert, and van Kreveld (1993) and Matousek.Expand