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A-priori upper bounds for the set covering problem

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Abstract

In this paper we present a new bound obtained with the probabilistic method for the solution of the set covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic results, and it depends only on the number of rows of the coefficient matrix and the row densities. We also consider the particular case of matrices that are almost block decomposable, and show how the bound may improve according to the particular decomposition adopted. Such final result may provide interesting indications for comparing different matrix decomposition strategies.

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Acknowledgments

This work has been supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Consiglio Nazionale delle Ricerche (CNR) (Scientific Cooperation Agreement CNR-CNPq 2012–2013), and FAPEMIG (Fundacão de Amparo à Pesquisa do Estado de Minas Gerais)-Programa Pesquisador Mineiro.

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, 00185, Rome, Italy

    Giovanni Felici

  2. Departamento de Estatistica-ICEx, UFMG, CP 702, Belo Horizonte, MG, 30161-970, Brazil

    Sokol Ndreca

  3. Departamento de Matemática-ICEx, UFMG, CP 702, Belo Horizonte, MG, 30161-970, Brazil

    Aldo Procacci

  4. Dipartimento di Matematica, Universita Tor Vergata di Roma, 00133, Rome, Italy

    Benedetto Scoppola

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  1. Giovanni Felici
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  2. Sokol Ndreca
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  3. Aldo Procacci
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  4. Benedetto Scoppola
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Correspondence to Giovanni Felici.

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Felici, G., Ndreca, S., Procacci, A. et al. A-priori upper bounds for the set covering problem. Ann Oper Res 238, 229–241 (2016). https://doi.org/10.1007/s10479-015-2069-0

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  • DOI: https://doi.org/10.1007/s10479-015-2069-0

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