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 …

This well-accepted introduction to computational geometry is a textbook for high-level
undergraduate and low-level graduate courses. The focus is on algorithms and hence the …

Exact algorithms for dealing with geometric objects are complicated, hard to implement in
practice, and slow. Over the last 20 years a theory of geometric approximation algorithms …

We present a simple randomized algorithm which solves linear programs with n constraints
and d variables in expected O (nde (d ln (n+ 1)) 1/4) time in the unit cost model (where we …

The presence of embedded electronics and communication capabilities as well as sensing
and control in smart devices has given rise to the novel concept of cyber-physical networks …

The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations
in which two or more players can make coalitions and obtain prizes and penalties. This …

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral,
or tetrahedral elements to optimize the shapes of adjacent elements. We show that many …

We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and
Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg …

In this paper we present a variety of problems in the interface between combinatorics and
geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these …

We develop algorithms for computing the smallest enclosing ball of a set of n balls in d-
dimensional space. Unlike previous methods, we explicitly address small cases (n= d+ 1) …