Advertisement

A Least-Resistance Path in Reasoning about Unstructured Overlay Networks

  • Giorgos Georgiadis
  • Marina Papatriantafilou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5704)

Abstract

Unstructured overlay networks for peer-to-peer applications combined with stochastic algorithms for clustering and resource location are attractive due to low-maintenance costs and inherent fault-tolerance and self-organizing properties. Moreover, there is a relatively large volume of experimental evidence that these methods are efficiency-wise a good alternative to structured methods, which require more sophisticated algorithms for maintenance and fault tolerance. However, currently there is a very limited selection of appropriate tools to use in systematically evaluating performance and other properties of such non-trivial methods.

Based on a well-known association between random walks and resistor networks, and building on a recently pointed-out connection with peer-to-peer networks, we tie-in a set of diverse techniques and metrics of both realms in a unifying framework. Furthermore, we present a basic set of tools to facilitate the analysis of overlay properties and the reasoning about algorithms for peer-to-peer networks. One of the key features of this framework is that it enables us to measure and contrast the local and global impact of algorithmic decisions in peer-to-peer networks. We provide example experimental studies that furthermore demonstrate its capabilities in the overlay network context.

Keywords

Random Walk Fault Tolerance Degree Node Weighted Graph Overlay Network 
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.
    Balakrishnan, H., Kaashoek, F.M., Karger, D., Morris, R., Stoica, I.: Looking up data in p2p systems. Commun. ACM 46(2), 43–48 (2003)CrossRefGoogle Scholar
  2. 2.
    Adamic, L.A., Lukose, R.M., Puniyani, A.R., Huberman, B.A.: Search in power-law networks. Phys. Rev. E 64, 46135 (2001)CrossRefGoogle Scholar
  3. 3.
    Ata, S., Murata, M., Gotoh, Y.: Replication methods for enhancing search performance in peer-to-peer services on power-law logical networks. In: Performance and Control of Next-Generation Communications Networks. SPIE, vol. 5244, pp. 76–85 (2003)Google Scholar
  4. 4.
    Gkantsidis, C., Mihail, M., Saberi, A.: Random walks in peer-to-peer networks. In: Proc. of 23rd Annual Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2004), March 2004, vol. 1 (2004)Google Scholar
  5. 5.
    Sarshar, N., Boykin, P.O., Roychowdhury, V.P.: Percolation search in power law networks: making unstructured peer-to-peer networks scalable. In: Proc. of the 4th International Conf. on Peer-to-Peer Computing, pp. 2–9 (2004)Google Scholar
  6. 6.
    Zhaoqing, J., Jinyuan, Y., Ruonan, R., Minglu, L.: Random walk search in unstructured p2p. J. Syst. Eng. 17(3), 648–653 (2006)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chockler, G., Melamed, R., Tock, Y., Vitenberg, R.: Spidercast: a scalable interest-aware overlay for topic-based pub/sub communication. In: Proc. of 2007 inaugural international conf. on Distributed event-based systems (DEBS 2007), pp. 14–25. ACM, New York (2007)CrossRefGoogle Scholar
  8. 8.
    Fraigniaud, P., Gauron, P., Latapy, M.: Combining the use of clustering and scale-free nature of user exchanges into a simple and efficient p2p system. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 1163–1172. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Voulgaris, S., Kermarrec, A.M., Massoulie, L.: Exploiting semantic proximity in peer-to-peer content searching. In: Proc. of 10th IEEE International Workshop on Future Trends of Distributed Computing Systems (FTDCS 2004), pp. 238–243 (2004)Google Scholar
  10. 10.
    Hughes, B.: Random Walks and Random Environments: Random Walks, vol. 1. Clarendon Press, Oxford (1995)zbMATHGoogle Scholar
  11. 11.
    Klein, D.J., Randić, M.: Resistance distance. J. Math. Chem. 12(1), 81–95 (1993)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bui, A., Sohier, D.: How to compute times of random walks based distributed algorithms. Fundamenta Informaticae 80(4), 363–378 (2007)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Sohier, D., Bui, A.: Hitting times computation for theoretically studying peer-to-peer distributed systems. In: Proc. of the 18th International Parallel and Distributed Processing Symposium (2004)Google Scholar
  14. 14.
    Telcs, A.: The Art of Random Walks. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  15. 15.
    Lv, Q., Cao, P., Cohen, E., Li, K., Shenker, S.: Search and replication in unstructured peer-to-peer networks. In: Proc. of the 16th International Conf. on Supercomputing (ICS 2002), pp. 84–95. ACM Press, New York (2002)Google Scholar
  16. 16.
    Barnett, S.: Matrices: Methods and Applications. Oxford University Press, Oxford (1990)zbMATHGoogle Scholar
  17. 17.
    Fiedler, M.: Algebraic connectivity of graphs. Czechoslovak Math. J. 23, 298–305 (1973)MathSciNetzbMATHGoogle Scholar
  18. 18.
    de Abreu, N.M.: Old and new results on algebraic connectivity of graphs. Linear Algebra and its Applications 423(1), 53–73 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Chung, F.: Spectral Graph Theory. CBMS Regional Conf. Series in Mathematics, vol. 92. AMS (1997)Google Scholar
  20. 20.
    Doyle, P.G., Snell, L.J.: Random Walks and Electrical Networks. Mathematical Association of America (December 1984)Google Scholar
  21. 21.
    Chandra, A.K., Raghavan, P., Ruzzo, W.L., Smolensky, R.: The electrical resistance of a graph captures its commute and cover times. In: Proc. of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 574–586. ACM Press, New York (1989)Google Scholar
  22. 22.
    Alexander, C., Sadiku, M.: Fundamentals of Electric Circuits. McGraw-Hill, New York (2006)Google Scholar
  23. 23.
    Fouss, F., Pirotte, A., Renders, J.M., Saerens, M.: Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation. IEEE Trans. Knowl. Data Eng. 19(3), 355–369 (2007)CrossRefGoogle Scholar
  24. 24.
    Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1-7), 107–117 (1998)CrossRefGoogle Scholar
  25. 25.
    Olfati-Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Georgiadis, G., Kirousis, L.: Lightweight centrality measures in networks under attack. In: Proc. of European Conf. on Complex Systems, ECCS (2005)Google Scholar
  27. 27.
    Madduri, K., Bader, D.A., Berry, J.W., Crobak, J.R., Hendrickson, B.A.: Multithreaded algorithms for processing massive graphs. In: Bader, D.A. (ed.) Petascale Computing: Algorithms and Applications. Chapman & Hall/CRC Computational Science Series, Boca Raton (2008)Google Scholar
  28. 28.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–98 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Ripeanu, M., Foster, I., Iamnitchi, A.: Mapping the gnutella network: Properties of large-scale peer-to-peer systems and implications for system design. IEEE Internet Comput. 6(1), 50–57 (2002)CrossRefGoogle Scholar
  30. 30.
    NVIDIA Corporation nvidia.com/cuda: NVIDIA CUDA Programming Guide. 2.0b edn. (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Giorgos Georgiadis
    • 1
  • Marina Papatriantafilou
    • 1
  1. 1.Department of Computer Science and EngineeringChalmers University of TechnologyGöteborgSweden

Personalised recommendations