Given a finite collection S of geometric objects such as hyperplanes or spheres in Rd, the
arrangement A (S) is the decomposition of Rd into connected open cells of dimensions 0 …

We give an algorithmic and lower bound framework that facilitates the construction of
subexponential algorithms and matching conditional complexity bounds. It can be applied to …

We investigate the family of intersection graphs of low density objects in low dimensional
Euclidean space. This family is quite general, includes planar graphs, and in particular is a …

The use of random samples to approximate properties of geometric configurations has been
an influential idea for both combinatorial and algorithmic purposes. This chapter considers …

Given a finite range space Σ=(X, R), with N=| X|+| R|, we present two simple algorithms,
based on the multiplicative-weight method, for computing a small-size hitting set or set cover …

Given a finite range space Σ=(X, R) Σ=(X, R), with N=| X|+| R| N=| X|+| R|, we present two
simple algorithms, based on the multiplicative-weight method, for computing a small-size …

Let F be a set of n objects in the plane and let G×(F) be its intersection graph. A balanced
clique-based separator of G×(F) is a set S consisting of cliques whose removal partitions …

We give an algorithmic and lower-bound framework that facilitates the construction of
subexponential algorithms and matching conditional complexity bounds. It can be applied to …

Understanding the behavior of basic sampling techniques and intrinsic geometric attributes
of data is an invaluable skill that is in high demand for both graduate students and …

Given a set of points P and a set of regions O, an incidence is a pair (p, o)∈ P× O such that
p∈ o. We obtain a number of new results on a classical question in combinatorial geometry …