Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
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)
Coja-Oghlan, A., Moore, C., Sanwalani, V.: Counting connected graphs and hypergraphs via the probabilistic method. Random Structure and Algorithms 31, 288–329 (2007)
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)
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)
Durrett, R.: Probability and examples, 3rd edn. (2005)
Darling, R.W.R., Norris, J.R.: Structure of large random hypergraphs. Ann. App. Probability 15(1A), 125–152 (2005)
Feller, W.: An introduction to probability theory and its applications. Wiley, Chichester (1950)
Janson, S., Łuczak, T., Ruciński, A.: Random Graphs. Wiley, Chichester (2000)
Mitzenmacher, M., Upfal, E.: Probability and Computing, Randomized Algorithms and Probabilistic Analysis. Cambridge Univ. Press, Cambridge (2005)
Karp, R.M.: The transitive closure of a random digraph. Random Structures and Algorithms 1, 73–93 (1990)
Molloy, M.: Cores in random hypergraphs and Boolean formulas. Random Structures and Algorithms 27(1), 124–135 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Coja-Oghlan, A., Onsjö, M., Watanabe, O. (2010). Propagation Connectivity of Random Hypergraphs. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2010 2010. Lecture Notes in Computer Science, vol 6302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15369-3_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-15369-3_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15368-6
Online ISBN: 978-3-642-15369-3
eBook Packages: Computer ScienceComputer Science (R0)