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A Continuous Characterization of Maximal Cliques in k-Uniform Hypergraphs

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Learning and Intelligent Optimization (LION 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5313))

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Abstract

In 1965 Motzkin and Straus established a remarkable connection between the local/global maximizers of the Lagrangian of a graph G over the standard simplex Δ and the maximal/maximum cliques of G. In this work we generalize the Motzkin-Straus theorem to k-uniform hypergraphs, establishing an isomorphism between local/global minimizers of a particular function over Δ and the maximal/maximum cliques of a k-uniform hypergraph. This theoretical result opens the door to a wide range of further both practical and theoretical applications, concerning continuous-based heuristics for the maximum clique problem on hypergraphs, as well as the discover of new bounds on the clique number of hypergraphs. Moreover we show how the continuous optimization task related to our theorem, can be easily locally solved by mean of a dynamical system.

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Authors and Affiliations

  1. Dipartimento di Informatica., Università Ca’ Foscari di Venezia, Italy

    Samuel Rota Bulò & Marcello Pelillo

Authors
  1. Samuel Rota Bulò
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  2. Marcello Pelillo
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Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of Bologna, Bologna, Italy

    Vittorio Maniezzo

  2. Università degli Studi di Trento, Trento, Italy

    Roberto Battiti

  3. Discrete Math and Complex Systems Department, Sandia National Laboratories, Albuquerque, New Mexico, USA

    Jean-Paul Watson

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Rota Bulò, S., Pelillo, M. (2008). A Continuous Characterization of Maximal Cliques in k-Uniform Hypergraphs. In: Maniezzo, V., Battiti, R., Watson, JP. (eds) Learning and Intelligent Optimization. LION 2007. Lecture Notes in Computer Science, vol 5313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92695-5_17

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  • DOI: https://doi.org/10.1007/978-3-540-92695-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92694-8

  • Online ISBN: 978-3-540-92695-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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