We consider a natural generalization of the classical minimum hitting set problem, the minimum hitting set of bundles problem (mhsb) which is defined as follows. We are given a set E = {e1, e2, . . . , en} of n elements. Each element ei (i = 1, . . . , n) has a non negative cost ci. A bundle b is a subset of E . We are also given a collection S = {S1, S2, . . . , Sm} of m sets of bundles. More ...

The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order O(c), but with the co...

Several approximation algorithms with proven performance guarantees have been proposed to find approximate solutions to classical combinatorial optimization problems. However, theoretical results may not reflect the experimental performance of the proposed algorithms. As a consequence, a question arises: how “far” from the theoretically proved performance are the experimental results?We conduct...

Databases containing varied linguistic features can be build by condensing large corpora; in this work we need to cover a set of phonetic units with a minimal set of natural phonetic sentences. With this aim in view we compare three set covering methods: the greedy method, its inverse which we call the spitting method, and the pair exchange method. Each method is defined with several criteria g...

In this paper, we study a class of set cover problems that satisfy a special property which we call the small neighborhood cover property. This class encompasses several well-studied problems including vertex cover, interval cover, bag interval cover and tree cover. We design unified distributed and parallel algorithms that can handle any set cover problem falling under the above framework and ...

When BDDs are used for propagation in a constraint solver with nogood recording, it is necessary to find a small subset of a given set of variable assignments that is enough for a BDD to imply a new variable assignment. We show that the task of finding such a minimum subset is NP-complete by reduction from the hitting set problem. We present a new algorithm for finding such a minimal subset, wh...

In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that hits intersects all of them The problem is NP hard It is not known whether there exists a polynomial time approximation algorithm for the hitting set problem with a nite performance ratio Special cases of the hitting set problem are described for which nite performance ratios a...

This paper uses a realistic problem taken from the telecommunication world as the basis for comparing di.erent combinatorial optimization algorithms. The problem recalls the minimum hitting set problem, and is solved with greedy-like, Darwinism and genetic algorithms. These three paradigms are described and analyzed with emphasis on the Darwinism approach, which is based on the computation of -...

A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n] to within o(1) error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hitting set pr...

The first part of this report describes the following result that, logarithmic approximation factor for hard capacitated set cover can be achieved from Wolsey's work [9], using a simpler and more intuitive analysis. We further show in our work, that O(log n) approximation factor can be achieved for the same problem by applying analysis of general set cover to analyze Wolsey's algorithm [5]. Thi...