J. Orestes Cerdeira

Computational aspects of algorithms for variable selection in the context of principal components

Variable selection consists in identifying a k-subset of a set of original variables that is optimal for a given criterion of adequate approximation to the whole data set. Several algorithms for the optimization problems resulting from three different criteria in the context of principal components analysis are considered, and computational results are presented.

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p>=3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete.

Requiring connectivity in the set covering problem

Given a bipartite graph with bipartition V and W, a cover is a subset C

Matroids and a forest cover problem

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A Combinatorial Approach to Assess the Separability of Clusters

V such that each node of W is adjacent to at least one node in C. The set covering problem seeks a minimum cardinality cover. Set covering has many practical applications. In the context of reserve selection for conservation of species, V is a set of candidate sites from a reserve network, W is the set of species to be protected, and the edges describe which species are represented in each site. Some covers however may assume spatial configurations which are not adequate for conservational purposes. Indeed, for sustainability reasons the fragmentation of existing natural habitats should be avoided, since this is recognized as being disruptive to the species adapted to the habitats. Thus, connectivity appears to be an important issue for protection of biological diversity. We therefore consider along with the bipartite graph, a graph G with node set V, describing the adjacencies of the elements of V, and we look for those covers C

Data depth for the uniform distribution

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