Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the memb...
A pants decomposition of an orientable surface is a collection of simple cycles that partition into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P...
We develop algorithms to compute Voronoi diagrams, shortest path maps, and the Fr´echet distance in the plane with polygonal obstacles. Distances between points are measured eithe...
Do convex obstacles in the plane always leave 3 separate escape routes? Here, an escape route is a locally geodesic path that avoids the obstacles; escape routes are separate if t...
David L. Millman, Matthew O'Meara, Jack Snoeyink, ...
We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computation...