Discrete Mathematics and Optimization Seminar

University of Toronto
Monday January 19th at 4.30pm
Burnside 1205

Title. Sublinear Geometric Algorithms.

Abstract. We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions.
We give optimal algorithms for detecting intersection of convex polygons and polyhedra, point location in two-dimensional
Delaunay triangulations and Voronoi diagrams, and ray shooting in convex polyhedra, all of which run in expected time O(sqrt{n}),
where n is the size of the input. We also provide sublinear solutions for the approximate evaluation of the volume of a convex polytope
in 3D and the length of the shortest path between two points on the boundary.

Joint work with Bernard Chazelle and Ding Liu (Princeton University)