The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define...
Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance...
Abstract. Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H2 . We then show that continuous isometry invariant s...
The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algo...
Pankaj K. Agarwal, Sariel Har-Peled, Meetesh Karia
In this paper, we resolve the smoothed and approximative complexity of low-rank quasi-concave minimization, providing both upper and lower bounds. As an upper bound, we provide th...