We establish significantly improved bounds on the performance of the greedy
algorithm for approximating MINIMUM SET COVER and MINIMUM PARTIAL COVER. Our
improvements result from a new approach to both problems. In particular,
(a) we improve the known bound on the performance ratio of the greedy ... more >>>

In this paper we study the approximability of boolean constraint
satisfaction problems. A problem in this class consists of some
collection of ``constraints'' (i.e., functions
$f:\{0,1\}^k \rightarrow \{0,1\}$); an instance of a problem is a set
of constraints applied to specified subsets of $n$ boolean
variables. Schaefer earlier ... more >>>

This paper continues the work initiated by Creignou [Cre95] and
Khanna, Sudan and Williamson [KSW96] who classify maximization
problems derived from boolean constraint satisfaction. Here we
study the approximability of {\em minimization} problems derived
thence. A problem in this framework is characterized by a
collection F ... more >>>

Given a finite set $S$ of points (i.e. the stations of a radio
network) on a $d$-dimensional Euclidean space and a positive integer
$1\le h \le |S|-1$, the \minrangeh{d} problem
consists of assigning transmission ranges to the stations so as
to minimize the total power consumption, provided ... more >>>

A cycle cover of a graph is a set of cycles such that every vertex is
part of exactly one cycle. An L-cycle cover is a cycle cover in which
the length of every cycle is in the set L. The weight of a cycle cover
of an edge-weighted graph ... more >>>

The main aim of randomized search heuristics is to produce good approximations of optimal solutions within a small amount of time. In contrast to numerous experimental results, there are only a few theoretical results on this subject.
We consider the approximation ability of randomized search for the class of ... more >>>

The width complexity measure plays a central role in Resolution and other propositional proof systems like Polynomial Calculus (under the name of degree). The study of width lower bounds is the most extended method for proving size lower bounds, and it is known that for these systems, proofs with small ... more >>>