Propagation Connectivity of Random Hypergraphs

  • Robert Berke
  • Mikael Onsjö
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5792)


We consider the average-case MLS-3LIN problem, the problem of finding a most likely solution for a given system of perturbed 3LIN-equations generated with equation probability p and perturbation probability q. Our purpose is to investigate the situation for certain message passing algorithms to work for this problem whp We consider the case q = 0 (no perturbation occurs) and analyze the execution of (a simple version of) our algorithm. For characterizing problem instances for which the execution succeeds, we consider their natural 3-uniform hypergraph representation and introduce the notion of “propagation connectivity”, a generalized connectivity property on 3-uniform hypergraphs. The execution succeeds on a given system of 3LIN-equations if and only if the representing hypergraph is propagation connected. We show upper and lower bounds for equation probability p such that propagation connectivity holds whp on random hypergraphs representing MLS-3LIN instances.


Random Graph Initial Assignment Equation Probability Propagation Connectivity Marked Vertex 
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 2009

Authors and Affiliations

  • Robert Berke
    • 1
  • Mikael Onsjö
    • 1
  1. 1.Dept. of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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