In this paper, we study the problem of finding a disk covering the largest number of red points, while avoiding all the blue points. We reduce it to the question of finding a deepest point in an… (More)

It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to… (More)

Dissecting Euclidean d -space with the power diagram of n weighted point sites partitions a given m -point set into clusters, one cluster for each region of the diagram. In this manner, an assignment… (More)

We show the existence of ε-nets of size O ( 1 ε log log 1 ε ) for planar point sets and axisparallel rectangular ranges. The same bound holds for points in the plane and “fat” triangular ranges and… (More)

We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3+ kn log2 k ) . This bound is almost tight in the worst case. We… (More)

We consider the problem of bounding the complexity of the fe-th level in an arran^ment of n curvra or surfM«s, a problem dual to, and «rtending, the iirell-known k-aet pmblem. (a) We review and… (More)

Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1, . . . , Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free… (More)