We review the recent progress in the design of efficient algorithms for various problems in
geometric optimization. We present several techniques used to attack these problems, such …

The arrangement of a finite collection of geometric objects is the decomposition of the space
into connected cells induced by them. We survey combinatorial and algorithmic properties of …

We describe general randomized reductions of certain geometric optimization problems to
their corresponding decision problems. These reductions increase the expected time …

In this paper we first prove the following combinatorial bound, concerning the complexity of
the vertical decomposition of the minimization diagram of trivariate functions: Let> be a …

We present a new approach to problems in geometric optimization that are traditionally
solved using the parametric-searching technique of Megiddo J. ACM, 30 (1983), pp. 852 …

A natural extension of point facility location problems are those problems in which facilities
are extensive, ie those that cannot be represented by isolated points but as some …

Any machine exposed to the Internet today is at the risk of being attacked and compromised.
Detecting attack attempts, be they successful or not, is important for securing networks …

" Based on a lecture series given by the authors at a satellite meeting of the 2006
International Congress of Mathematicians and on many articles written by them and their …

We address a fundamental problem arising from analysis of biomolecular sequences. The
input consists of two numbers w min and w max and a sequence S of n number pairs (ai, wi) …

We consider the following two instances of the projective clustering problem: Given a set S
of n points in R d and an integer k> 0, cover S by k slabs (respectively d-cylinders) so that …