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...

Eigenvectors of the Laplacian of a cycle graph exhibit the sinusoidal characteristics of the standard DFT basis, and signals defined on such graphs are amenable to linear shift invariant (LSI) operations. In this paper we propose to reduce a generic graph to its vertex-disjoint cycle cover, i.e., a set of subgraphs that are cycles, that together contain all vertices of the graph, and no two sub...

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...

Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (“propositions”) of cover systems that use an orthogonality relation to interpret the negations. The variety of Grishin algebras is shown to be closed ...

by the publisher. No part of this journal may be reproduced or used in any form or by any means without written permission from the publisher, except for noncommercial, educational use including classroom teaching purposes. Product or company names used in this journal are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownershi...

A finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. In this paper the covering number of the Mathieu group M24 is show...

The Antarctic contribution to sea-level rise has long been uncertain. While regional variability in ice dynamics has been revealed, a picture of mass changes throughout the continental ice sheet is lacking. Here, we use satellite radar altimetry to measure the elevation change of 72% of the grounded ice sheet during the period 1992-2003. Depending on the density of the snow giving rise to the o...