We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest su...
We present two new fundamental lower bounds on the worst-case combinatorial complexity of sets of free lines and sets of maximal free line segments in the presence of balls in thr...
We define a fundamental domain for a linear programming relaxation of a combinatorial integer program which is symmetric under a group action. We then describe a straightforward w...
Topology modification of hexahedral meshes has been considered difficult due to the propagation of topological modifications non-locally. We address this problem by working in the...
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the p...
David Cohen-Steiner, Herbert Edelsbrunner, John Ha...