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Knowledge and Information Systems

, Volume 38, Issue 2, pp 469–490 | Cite as

Expansion and decentralized search in complex networks

  • Arun S. Maiya
  • Tanya Y. Berger-Wolf
Regular paper

Abstract

Borrowing from concepts in expander graphs, we study the expansion properties of real-world, complex networks (e.g., social networks, unstructured peer-to-peer, or P2P networks) and the extent to which these properties can be exploited to understand and address the problem of decentralized search. We first produce samples that concisely capture the overall expansion properties of an entire network, which we collectively refer to as the expansion signature. Using these signatures, we find a correspondence between the magnitude of maximum expansion and the extent to which a network can be efficiently searched. We further find evidence that standard graph-theoretic measures, such as average path length, fail to fully explain the level of “searchability” or ease of information diffusion and dissemination in a network. Finally, we demonstrate that this high expansion can be leveraged to facilitate decentralized search in networks and show that an expansion-based search strategy outperforms typical search methods.

Keywords

Expansion Decentralized search P2P Peer-to-peer networks Social network analysis Complex networks Graph mining Expander graphs 

References

  1. 1.
    Adamic LA, Lukose RM, Puniyani AR, Huberman BA (2001) Search in power-law networks. Phys Rev E 64(4):046135+Google Scholar
  2. 2.
    Barabasi A-L, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512CrossRefMathSciNetGoogle Scholar
  3. 3.
    Barret CL, Eubank SG, Smith JP (2007) Fighting infectious diseases (Scientific American). Rosen Publishing Group, New YorkGoogle Scholar
  4. 4.
    Boguna M, Krioukov D, Claffy KC (2008) Navigability of complex networks. Nat Phys 5(1):74–80CrossRefGoogle Scholar
  5. 5.
    Chierichetti F, Kumar R, Tomkins A (2010) Max-cover in map-reduce. In: Proceedings of the 19th international conference on world wide web, WWW ’10. New York, NY, USA. ACM, pp 231–240Google Scholar
  6. 6.
    Chierichetti F, Lattanzi S, Panconesi A (2010) Rumour spreading and graph conductance. In: SODA 2010Google Scholar
  7. 7.
    Daly EM, Haahr M (2007) Social network analysis for routing in disconnected delay-tolerant MANETs. In: Proceedings of the 8th ACM international symposium on mobile ad hoc networking and computing, MobiHoc ’07. New York, NY, USA. ACM, pp 32–40Google Scholar
  8. 8.
    Erdös P, Rényi A (1959) On random graphs, I. Publicationes Mathematicae (Debrecen) 6:290–297zbMATHMathSciNetGoogle Scholar
  9. 9.
    Feige U (1998) A threshold of ln n for approximating set cover. J ACM 45(4):634–652CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness (series of books in the mathematical sciences), 1st edn. W. H. Freeman & Co Ltd, San Francisco, CAGoogle Scholar
  11. 11.
    Gehrke J, Ginsparg P, Kleinberg J (2003) Overview of the 2003 KDD Cup. SIGKDD Explor Newsl 5(2):149–151CrossRefGoogle Scholar
  12. 12.
    Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Guha S, Khuller S (1998) Approximation algorithms for connected dominating sets. Algorithmica 20(4):374–387CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Hochbaum DS (ed) (1997) Approximation algorithms for NP-hard problems. PWS Publishing Co., Boston, MAGoogle Scholar
  15. 15.
    Hochbaum DS, Pathria A (1998) Analysis of the greedy approach in problems of maximum k-coverage. Nav Res Logist (NRL) 45(6):615–627CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Hoory S, Linial N, Wigderson A (2006) Expander graphs and their applications. Bull Am Math Soc 43:439–561Google Scholar
  17. 17.
    Hui KYK, Lui JCS, Yau DKY (2006) Small-world overlay P2P networks: construction, management and handling of dynamic flash crowds. Comput Netw 50(15):2727–2746CrossRefzbMATHGoogle Scholar
  18. 18.
    Jiang S, Guo L, Zhang X, Wang H (2008) LightFlood: minimizing redundant messages and maximizing scope of peer-to-peer search. IEEE Trans Parallel Distrib Syst 19(5):601–614CrossRefGoogle Scholar
  19. 19.
    Jin S, Jiang H (2007) Novel approaches to efficient flooding search in peer-to-peer networks. Comput Netw 51(10):2818–2832CrossRefzbMATHGoogle Scholar
  20. 20.
    Kannan R, Vempala S, Vetta A (2004) On clusterings: good, bad and spectral. J ACM 51(3):497–515CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Kleinberg J (2000) The small-world phenomenon: an algorithmic perspective. In: Proceedings of the 32nd ACM symposium on theory of computing, May 2000Google Scholar
  22. 22.
    Kleinberg J (2006) Complex networks and decentralized search algorithms. In: International Congress of Mathematicians (ICM)Google Scholar
  23. 23.
    Kleinfeld J (2002) Could it be a big world after all? the ’six degrees of separation’ myth. Society, Apr 2002Google Scholar
  24. 24.
    Klimt B, Yang Y (2004) The enron corpus: a new dataset for email classification research. Mach Learn ECML 2004:217–226Google Scholar
  25. 25.
    Leskovec J, Kleinberg J, Faloutsos C (2005) Graphs over time: densification laws, shrinking diameters and possible explanations. In: KDD ’05: proceedings of the eleventh ACM SIGKDD international conference on knowledge discovery in data mining, pp 177–187Google Scholar
  26. 26.
    Leskovec J, Lang KJ, Dasgupta A, Mahoney MW (2008) Statistical properties of community structure in large social and information networks. In: Proceedings of the 17th international conference on world wide web, WWW ’08. New York, NY, USA. ACM, pp 695–704Google Scholar
  27. 27.
    Li X, Wu J (2006) Searching techniques in peer-to-peer networks. In: Wu J (ed) Handbook of theoretical and algorithmic aspects of ad hoc, sensor, and peer-to-peer networks. Auerbach, New YorkGoogle Scholar
  28. 28.
    Liben-Nowell D, Novak J, Kumar R, Raghavan P, Tomkins A (2005) Geographic routing in social networks. Proc Natl Acad Sci USA 102(33):11623–11628CrossRefGoogle Scholar
  29. 29.
    Maiya AS, Berger-Wolf TY (2010) Sampling community structure. In: WWW ’10: proceedings of the 19th international conference on the world wide web, Apr 2010Google Scholar
  30. 30.
    Maiya AS, Berger-Wolf TY (2011) Benefits of bias: towards better characterization of network sampling. In: Proceedings of the 17th ACM SIGKDD international conference on knowledge discovery and data mining, KDD ’11. New York, NY, USA. ACM, pp 105–113Google Scholar
  31. 31.
    Milgram S (1967) The small world problem. Psychol Today 2:60–67Google Scholar
  32. 32.
    Mitra B (2009) Technological networks. In: Ganguly N, Deutsch A, Mukherjee A (eds) Dynamics on and of complex networks, chapter 15. Birkhäuser Boston, Boston, pp 253–274CrossRefGoogle Scholar
  33. 33.
    Nemhauser GL, Wolsey LA, Fisher ML (1978) An analysis of approximations for maximizing submodular set functionsI. Math Program 14(1):265–294CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E (Statistical, Nonlinear, and Soft Matter Physics) 74(3):036104+Google Scholar
  35. 35.
    Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(3):036106+Google Scholar
  36. 36.
    Richardson M, Agrawal R, Domingos P (2003) Trust management for the semantic web. In: International semantic web conference, pp 351–368Google Scholar
  37. 37.
    Ripeanu M, Foster I, Iamnitchi A (2002) Mapping the gnutella network: properties of large-scale peer-to-peer systems and implications for system design. arXiv:cs/0209028v1 [cs.DC] Sept 2002Google Scholar
  38. 38.
    Schmid S, Wattenhofer R (2007) Structuring unstructured peer-to-peer networks. In: Aluru S, Parashar M, Badrinath R, Prasanna VK (eds) High performance computing HiPC 2007, vol 4873 of lecture notes in computer science, chapter 40. Springer, Berlin, pp 432–442Google Scholar
  39. 39.
    Tsoumakos D, Roussopoulos N (2006) Analysis and comparison of P2P search methods. In: InfoScale ’06: proceedings of the 1st international conference on scalable information systems, New York, NY, USA. ACM, pp 25+Google Scholar
  40. 40.
    Wasserman S, Faust K (2005) Models and methods in social network analysis (structural analysis in the social sciences). Cambridge University Press, CambridgeGoogle Scholar
  41. 41.
    Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393(6684):440–442CrossRefGoogle Scholar
  42. 42.
    Wu J, Li H (1999) On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of the 3rd international workshop on discrete algorithms and methods for mobile computing and communications, DIALM ’99, New York, NY, USA. ACM, pp 7–14Google Scholar
  43. 43.
    Yang B, Molina HG (2002) Improving search in peer-to-peer networks. In: ICDCS ’02: proceedings of the 22nd international conference on distributed computing systems (ICDCS’02), Washington, DC, USA, IEEE Computer Society, pp 5+Google Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.Institute for Defense AnalysesAlexandriaUSA
  2. 2.University of Illinois at ChicagoChicagoUSA

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