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Inverting the Achlioptas rule for explosive percolation

R. A. da Costa1, S. N. Dorogovtsev1,2, A. V. Goltsev1,2, and J. F. F. Mendes1

  • 1Departamento de Física da Universidade de Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • 2A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia

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Phys. Rev. E 91, 042130 – Published 23 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042130

Abstract

In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set of anomalous features. We explore a process with the opposite selection rule, in which the biggest clusters of the randomly chosen ones merge together. We develop a theory of this kind of percolation based on the Smoluchowsky equation, find the percolation threshold, and describe the scaling properties of this continuous transition, namely, the critical exponents and amplitudes, and scaling functions. We show that, qualitatively, this transition is similar to the ordinary percolation one, though occurring in less connected systems.

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Phys. Rev. E 91, 042130– Published 23 April, 2015
  • Received 18 February 2015

©2015 American Physical Society

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