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Phase Transitions for the Cavity Approach to the Clique Problem on Random Graphs

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Abstract

We give a rigorous proof of two phase transitions for a disordered statistical mechanics system used to define an algorithm to find large cliques inside Erdös random graphs. Such a system is a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory.

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Authors and Affiliations

  1. LATP, CNRS, Université de Provence, 39 rue F. Joliot-Curie, 13013, Marseille, France

    Alexandre Gaudillière

  2. Dipartimento di Matematica, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, 00133, Rome, Italy

    Benedetto Scoppola

  3. Dipartimento di Matematica, University of Rome “Roma Tre”, Largo San Murialdo, 1, 00146, Rome, Italy

    Elisabetta Scoppola

  4. Dipartimento di Fisica, University of Rome “La Sapienza”, P.le Aldo Moro, 2, 00185, Rome, Italy

    Massimiliano Viale

Authors
  1. Alexandre Gaudillière
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  2. Benedetto Scoppola
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  3. Elisabetta Scoppola
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  4. Massimiliano Viale
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Corresponding author

Correspondence to Elisabetta Scoppola.

Additional information

Supported by GDRE 224 GREFI-MEFI and the European Research Council through the “Advanced Grant” PTRELSS 228032.

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Gaudillière, A., Scoppola, B., Scoppola, E. et al. Phase Transitions for the Cavity Approach to the Clique Problem on Random Graphs. J Stat Phys 145, 1127–1155 (2011). https://doi.org/10.1007/s10955-011-0336-2

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  • DOI: https://doi.org/10.1007/s10955-011-0336-2

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