DCG
2008
13 years 11 months ago
2008
For convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volum...
DCG
2008
13 years 11 months ago
2008
DCG
2008
13 years 11 months ago
2008
We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . In particular, we show that a family of n 2d disjoint unit balls in Rd has a line transversal if,...
DCG
2008
13 years 11 months ago
2008
We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces...
DCG
2008
13 years 11 months ago
2008
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling...
DCG
2008
13 years 11 months ago
2008
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the nu...
DCG
2008
13 years 11 months ago
2008
Two-dimensional constrained Delaunay triangulations are geometric structures that are popular for interpolation and mesh generation because they respect the shapes of planar domai...
DCG
2008
13 years 11 months ago
2008
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that t...
DCG
2008
13 years 11 months ago
2008
Let P be a set of n points in Rd . A subset S of P is called a (k, )-kernel if for every direction, the direction width of S -approximates that of P, when k "outliers" c...
DCG
2008
13 years 11 months ago
2008
We prove that for d 3, the 1-skeleton of any (d - 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette's lower b...