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Petersen Graph is Uniformly Most-Reliable

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Machine Learning, Optimization, and Big Data (MOD 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10710))

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Abstract

A celebrated problem in network optimization is the all-terminal reliability maximization. We want to communicate a fixed number n of terminals, but we have a fixed budget constraint m. The goal is to build m links such that the all-terminal reliability is maximized in the resulting graph. In such case, the result is a uniformly most-reliable graph. The discovery of these graphs is a challenging problem that launched an interplay between extremal graph theory and computational optimization.

In this paper, we mathematically prove that Petersen graph is uniformly most-reliable. The paper is closed with a conjecture on the existence of other uniformly most-reliable graphs.

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Acknowledgements

This work is partially supported by Project 395 CSIC I+D Sistemas Binarios Estocásticos Dinámicos. We wish to thank Dr. Louis Petingi for his valuable comments on t-optimality throughout the writing of this manuscript.

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Authors and Affiliations

  1. Facultad de Ingeniería, Instituto de Matemática y Estadística, IMERL, Universidad de la República, Montevideo, Uruguay

    Guillermo Rela, Franco Robledo & Pablo Romero

Authors
  1. Guillermo Rela
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  2. Franco Robledo
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  3. Pablo Romero
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Corresponding author

Correspondence to Guillermo Rela .

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Editors and Affiliations

  1. University of Catania, Catania, Italy

    Giuseppe Nicosia

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. University of Catania, Catania, Italy

    Giovanni Giuffrida

  4. Harvard University, Cambridge, MA, USA

    Renato Umeton

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Rela, G., Robledo, F., Romero, P. (2018). Petersen Graph is Uniformly Most-Reliable. In: Nicosia, G., Pardalos, P., Giuffrida, G., Umeton, R. (eds) Machine Learning, Optimization, and Big Data. MOD 2017. Lecture Notes in Computer Science(), vol 10710. Springer, Cham. https://doi.org/10.1007/978-3-319-72926-8_35

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  • DOI: https://doi.org/10.1007/978-3-319-72926-8_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72925-1

  • Online ISBN: 978-3-319-72926-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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