Let C be a set of geometric objects in Rd. The combinatorial complexity of the union of C is
the total number of faces of all dimensions on its boundary. We survey the known upper …

We show that the combinatorial complexity of the union of n infinite cylinders in ℝ 3, having
arbitrary radii, is O (n 2+ ε), for any ε> 0; the bound is almost tight in the worst case, thus …

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 …

We prove that the union complexity of a set of n constant-complexity locally fat objects
(which can be curved and/or non-convex) in the plane is O (λ t+ 2 (n) log n), where t is the …

A simplex spanned by a colored point set in Euclidean d-space is colorful if all vertices have
distinct colors. The union of all full-dimensional colorful simplices spanned by a colored …

Computational geometry is the branch of theoretical computer science that deals with
algorithms and data structures for geometric objects. The most basic geometric objects …

In this thesis we study a variety of problems in computational and combinatorial geometry,
which involve arrangements of geometric objects in the plane and in higher dimensions …

Turán and Ramsey Type Problems on Geometric Objects Page 1 Turán and Ramsey Type
Problems on Geometric Objects by Andrew Suk A dissertation submitted in partial fulfillment …

Arrangements in Geometry: Recent Advances and Challenges* Page 1 Arrangements in
Geometry: Recent Advances and Challenges* Micha Sharir School of Computer Science …

A simplex spanned by a colored point set in Euclidean d-space is colorful if all vertices have
distinct colors. The union of all full-dimensional colorful simplices spanned by a colored …