We consider the problem of computing minimum geometric hitting sets in which, given a set
of geometric objects and a set of points, the goal is to compute the smallest subset of points …

We present approximation algorithms for maximum independent set of pseudo-disks in the
plane, both in the weighted and unweighted cases. For the unweighted case, we prove that …

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 …

The minimum-weight set cover problem is widely known to be O (log n)-approximable, with
no improvement possible in the general case. We take the approach of exploiting problem …

We consider the following general scheduling problem. The input consists of n jobs, each
with an arbitrary release time, size, and monotone function specifying the cost incurred when …

We study several geometric set cover and set packing problems involving configurations of
points and geometric objects in Euclidean space. We show that it is APX-hard to compute a …

The motivation for writing this book came from our previous research works on sensor
coverage. They received a large number of citations and this number grows rapidly each …

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 …

We consider the problem of finding a lowest cost dominating set in a given disk graph
containing n disks. The problem has been extensively studied on subclasses of disk graphs …

Set cover and hitting set are fundamental problems in combinatorial optimization which are
well-studied in the offline, online, and dynamic settings. We study the geometric versions of …