We solve several fundamental geometric problems under a new streaming model recently proposed by Ruhl et al. [2, 12]. In this model, in one pass the input stream can be scanned to ...
Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restri...
We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or ...
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Color red and blue the n vertices of a convex polytope P in R3 . Can we compute the convex hull of each color class in o(n log n)? What if we have χ > 2 colors? What if the co...