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Expander Properties and the Cover Time of Random Intersection Graphs

  • Sotiris E. Nikoletseas
  • Christoforos Raptopoulos
  • Paul G. Spirakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

Abstract

We investigate important combinatorial and algorithmic properties of G n, m, p random intersection graphs. In particular, we prove that with high probability (a) random intersection graphs are expanders, (b) random walks on such graphs are “rapidly mixing” (in particular they mix in logarithmic time) and (c) the cover time of random walks on such graphs is optimal (i.e. it is Θ(n logn)). All results are proved for p very close to the connectivity threshold and for the interesting, non-trivial range where random intersection graphs differ from classical G n, p random graphs.

Keywords

Random Walk Random Graph Hamilton Cycle Markov Chain Monte Carlo Method Full Paper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sotiris E. Nikoletseas
    • 1
    • 2
  • Christoforos Raptopoulos
    • 1
    • 2
  • Paul G. Spirakis
    • 1
    • 2
  1. 1.Computer Technology Institute, P.O. Box 1122, 26110 PatrasGreece
  2. 2.University of Patras, 26500 PatrasGreece

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