We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is defined for investigating the performance of a simple algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for edge probability of random 3-uniform hypergraphs such that the propagation connectivity holds. Based on our analysis, we also show the way to implement the simple algorithm so that it runs in linear time on average.


Random Walk Constraint Satisfaction Problem Giant Component Good Pair Propagation Connectivity 
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  1. [BCK07]
    Behrisch, M., Coja-Oghlan, A., Kang, M.: Local limit theorems for the giant component of random hypergraphs. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 341–352. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. [BO09]
    Berke, R., Onsjö, M.: Propagation connectivity of random hyptergraphs. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 117–126. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. [CMV07]
    Coja-Oghlan, A., Moore, C., Sanwalani, V.: Counting connected graphs and hypergraphs via the probabilistic method. Random Structure and Algorithms 31, 288–329 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [CM04]
    Connamacher, H., Molloy, M.: The exact satisfiability threshold for a potentially intractable random constraint satisfaction problem. In: Proc. 45th Annual Symposium on Foundations of Computer Science (FOCS 2004), pp. 590–599. IEEE, Los Alamitos (2004)Google Scholar
  5. [COW10]
    Coja-Oghlan, A., Onsjö, M., Watanabe, O.: Propagation connectivity of random hypergraphs, Research Report C-271, Dept. Math. Comput. Sci., Tokyo Inst. of Tech. (2010)Google Scholar
  6. [D05]
    Durrett, R.: Probability and examples, 3rd edn. (2005)Google Scholar
  7. [DN05]
    Darling, R.W.R., Norris, J.R.: Structure of large random hypergraphs. Ann. App. Probability 15(1A), 125–152 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Fe50]
    Feller, W.: An introduction to probability theory and its applications. Wiley, Chichester (1950)zbMATHGoogle Scholar
  9. [JLR00]
    Janson, S., Łuczak, T., Ruciński, A.: Random Graphs. Wiley, Chichester (2000)zbMATHGoogle Scholar
  10. [MU05]
    Mitzenmacher, M., Upfal, E.: Probability and Computing, Randomized Algorithms and Probabilistic Analysis. Cambridge Univ. Press, Cambridge (2005)zbMATHGoogle Scholar
  11. [Kar90]
    Karp, R.M.: The transitive closure of a random digraph. Random Structures and Algorithms 1, 73–93 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [Mol05]
    Molloy, M.: Cores in random hypergraphs and Boolean formulas. Random Structures and Algorithms 27(1), 124–135 (2005)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  • Mikael Onsjö
    • 2
  • Osamu Watanabe
    • 2
  1. 1.Mathematics and Computer ScienceUniversity of WarwickCoventryUK
  2. 2.Department of Mathematical and Computing SciencesTokyo Institute of Technology

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