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The Traveling Salesman Problem and the Gnedenko Theorem

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New Advances in Statistical Modeling and Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

The traveling salesman problem (TSP) has three characteristics common to most problems, which have attracted and intrigued mathematicians: the simplicity of its definition, the wealth of its applications, and the inability to find its optimal solution in polynomial-time.In this paper, we provide point and interval estimates for the optimal cost of several instances of the TSP, by using the solutions obtained by running four approximate algorithms—the 2-optimal and 3-optimal algorithms and their greedy versions—and considering the three-parameter Weibull model, whose location parameter represents the (unknown) optimal cost of the TSP.

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Acknowledgments

The first author would like to thank Fundação Calouste Gulbenkian for the opportunity to study this topic within the scope of the program “Novos Talentos em Matemática.”

This work received financial support from Portuguese National Funds through FCT (Fundação para a Ciência e a Tecnologia) within the scope of project PEst-OE/MAT/UI0822/2011.

The authors are grateful to the referees for their valuable suggestions and comments.

Author information

Authors and Affiliations

  1. Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal

    Tiago Salvador

  2. CEMAT and Mathematics Department, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal

    Manuel Cabral Morais

Authors
  1. Tiago Salvador
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  2. Manuel Cabral Morais
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Corresponding author

Correspondence to Manuel Cabral Morais .

Editor information

Editors and Affiliations

  1. CEMAT and Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    António Pacheco

  2. CEAUL and School of Technology and Management, Polytechnic Institute of Leiria, Leiria, Portugal

    Rui Santos

  3. CEMAT and Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Maria do Rosário Oliveira

  4. CEAUL and Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Carlos Daniel Paulino

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Salvador, T., Morais, M.C. (2014). The Traveling Salesman Problem and the Gnedenko Theorem. In: Pacheco, A., Santos, R., Oliveira, M., Paulino, C. (eds) New Advances in Statistical Modeling and Applications. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05323-3_19

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