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 …

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 …

This chapter presents a general construction of the free energy function for the two‐
dimensional lattice heteropolymer model widely used to study the dynamics of proteins. It …

We describe a new technique for proving the existence of small μ-nets for hypergraphs
satisfying certain simple conditions. The technique is particularly useful for proving o (1/μ log …

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 …

We study the planar version of Minimum-Weight Set Cover, where one has to cover a given
set of points with a minimum-weight subset of a given set of planar objects. For the unit …

Can a combinatorial optimization problem be approximated better if it is determined by a
system of geometric objects? Many combinatorial optimization problems are NP-hard to …

Given a set system (X, R), the hitting set problem is to find a smallest-cardinality subset H⊆
X, with the property that each range R∈ R has a non-empty intersection with H. We present …

We consider the problem of finding a minimum-size hitting set in a range space F=(Q, R)
defined by a measure on a family of subsets of an infinite set R. We observe that, under …

The problem of an optimal cover of sets in three-dimensional Euclidian space by the union
of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is …