Advertisement

Node Sampling Using Random Centrifugal Walks

  • Andrés Sevilla
  • Alberto Mozo
  • Antonio Fernández Anta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7702)

Abstract

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the source, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it.

Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes’ weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter.

Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source.

The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution.

Keywords

Span Tree Connected Network Overlay Network Attachment Point Node Sampling 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Awan, A., Ferreira, R.A., Jagannathan, S., Grama, A.: Distributed uniform sampling in unstructured peer-to-peer networks. In: HICSS. IEEE CS (2006)Google Scholar
  2. 2.
    Bertier, M., Bonnet, F., Kermarrec, A.M., Leroy, V., Peri, S., Raynal, M.: D2HT: The best of both worlds, integrating RPS and DHT. In: EDCC. IEEE CS (2010)Google Scholar
  3. 3.
    Bonnet, F., Kermarrec, A.-M., Raynal, M.: Small-World Networks: From Theoretical Bounds to Practical Systems. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 372–385. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Bui, M., Butelle, F., Lavault, C.: A distributed algorithm for constructing a minimum diameter spanning tree. J. Parallel Distrib. Comput. (May 2004)Google Scholar
  5. 5.
    Busnel, Y., Beraldi, R., Baldoni, R.: On the uniformity of peer sampling based on view shuffling. Journal of Parallel and Distributed Computing (2011)Google Scholar
  6. 6.
    Elkin, M.: A faster distributed protocol for constructing a minimum spanning tree. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, Philadelphia, PA, USA (2004)Google Scholar
  7. 7.
    Fraigniaud, P., Giakkoupis, G.: On the searchability of small-world networks with arbitrary underlying structure. In: Schulman, L.J. (ed.) STOC. ACM (2010)Google Scholar
  8. 8.
    Gfeller, B., Santoro, N., Widmayer, P.: A distributed algorithm for finding all best swap edges of a minimum-diameter spanning tree. IEEE Trans. Dependable Secur. Comput. (January 2011)Google Scholar
  9. 9.
    Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Walking in facebook: A case study of unbiased sampling of osns. In: INFOCOM, pp. 2498–2506. IEEE (2010)Google Scholar
  10. 10.
    Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Practical recommendations on crawling online social networks. IEEE Journal on Selected Areas in Communications (October 2011)Google Scholar
  11. 11.
    Gurevich, M., Keidar, I.: Correctness of gossip-based membership under message loss. SIAM J. Comput. 39(8) (December 2010)Google Scholar
  12. 12.
    Jelasity, M., Voulgaris, S., Guerraoui, R., Kermarrec, A.-M., van Steen, M.: Gossip-based peer sampling. ACM Trans. Comput. Syst. 25(3) (2007)Google Scholar
  13. 13.
    Kempe, D., Kleinberg, J.M., Demers, A.J.: Spatial gossip and resource location protocols. J. ACM 51(6), 943–967 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Kleinberg, J.M.: Navigation in a small world. Nature 406(6798) (August 2000)Google Scholar
  15. 15.
    Lee, C.-H., Xu, X., Eun, D.Y.: Beyond random walk and metropolis-hastings samplers: why you should not backtrack for unbiased graph sampling. In: SIGMETRICS 2012. ACM (2012)Google Scholar
  16. 16.
    Milić, D., Braun, T.: Netice9: A stable landmark-less network positioning system. In: 2010 IEEE 35th Conference on Local Computer Networks (October 2010)Google Scholar
  17. 17.
    Sevilla, A., Mozo, A., Lorenzo, M.A., López-Presa, J.L., Manzano, P., Fernández Anta, A.: Biased Selection for Building Small-World Networks. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 32–47. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Zhong, M., Shen, K.: Random walk based node sampling in self-organizing networks. SIGOPS Oper. Syst. Rev. 40, 49–55 (2006)CrossRefGoogle Scholar
  19. 19.
    Sevilla, A., Mozo, A., Fernández Anta, A.: Node Sampling using Random Centrifugal Walks. CoRR, abs/1107.1089, version 3 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrés Sevilla
    • 1
  • Alberto Mozo
    • 2
  • Antonio Fernández Anta
    • 3
  1. 1.Dpto Informática AplicadaU. Politécnica de MadridMadridSpain
  2. 2.Dpto Arquitectura y Tecnología de ComputadoresU. Politécnica de MadridMadridSpain
  3. 3.Institute IMDEA NetworksMadridSpain

Personalised recommendations