Abstract
We study the problem of maintaining a given distribution of random graphs under an arbitrary sequence of vertex insertions and deletions. Since our goal is to model the evolution of dynamic logical networks, we work in a local model where we do not have direct access to the list of all vertices. Instead, we assume access to a global primitive that returns a random vertex, chosen uniformly from the whole vertex set. In this preliminary work, we focus on a simple model of uniform directed random graphs where all vertices have a fixed outdegree. We describe and analyze several algorithms for the maintenance task; the most elaborate of our algorithms are asymptotically optimal.
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References
Frankel, J., Pepper, T.: The gnutella project, http://www.gnutelliums.com/
Bennett, K., Stef, T., Grothoff, C., Horozov, T., Patrascu, I.: The gnet whitepaper. Technical report, Purdue University (2002)
Clarke, I., Sandberg, O., Wiley, B., Hong, T.W.: Freenet: A distributed anonymous information storage and retrieval system. In: Federrath, H. (ed.) Designing Privacy Enhancing Technologies. LNCS, vol. 2009, pp. 46–66. Springer, Heidelberg (2001)
Liben-nowell, D., Balakrishnan, H., Karger, D.: Analysis of the evolution of peer-to-peer systems. In: ACM Symposium on Principles of Distributed Computing, pp. 233–242 (2002)
Pandurangan, G., Raghavan, P., Upfal, E.: Building low-diameter p2p networks. In: FOCS, pp. 492–499 (2001)
Cooper, C., Dyer, M., Greenhill, C.: Sampling regular graphs and a peer-to-peer network. Comb. Probab. Comput. 16(4), 557–593 (2007)
Bourassa, V., Holt, F.B.: Swan: Small-world wide area networks. In: International Conference on Advances in Infracstructure, SSGRR-2003s (2003)
Seidel, R., Aragon, C.R.: Randomized search trees. Algorithmica 16(4/5), 464–497 (1996)
MartÃnez, C., Roura, S.: Randomized binary search trees. J. ACM 45(2), 288–323 (1998)
Pugh, W.: Skip lists: A probabilistic alternative to balanced trees. Commun. ACM 33(6), 668–676 (1990)
Stoica, I., Morris, R., Karger, D., Kaashoek, M.F., Balakrishnan, H.: Chord: A scalable peer-to-peer lookup service for internet applications. SIGCOMM Comput. Commun. Rev. 31(4), 149–160 (2001)
Cooper, C., Klasing, R., Radzik, T.: A randomized algorithm for the joining protocol in dynamic distributed networks. Theor. Comput. Sci. 406(3), 248–262 (2008)
Knuth, D.E., Yao, A.C.: The complexity of nonuniform random number generation. In: Proceedings of Symposium on Algorithms and Complexity, pp. 357–428. Academic Press, New York (1976)
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Duchon, P., Duvignau, R. (2014). Local Update Algorithms for Random Graphs. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_32
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DOI: https://doi.org/10.1007/978-3-642-54423-1_32
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