A Constant-Factor Approximation Algorithm for the Link Building Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6509)


In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP. We present a polynomial time algorithm yielding a PageRank value within a constant factor from the optimal. We also consider the naive algorithm where we choose backlinks from nodes with high PageRank values compared to the outdegree and show that the naive algorithm performs much worse on certain graphs compared to the constant factor approximation scheme.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avrachenkov, K., Litvak, N.: The effect of new links on Google PageRank. Stochastic Models 22(2), 319–331 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bianchini, M., Gori, M., Scarselli, F.: Inside pagerank. ACM Transactions on Internet Technology 5(1), 92–128 (2005)CrossRefGoogle Scholar
  3. 3.
    Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems 30(1-7), 107–117 (1998)CrossRefGoogle Scholar
  4. 4.
    Dekerchove, C., Ninove, L., Vandooren, P.: Maximizing PageRank via outlinks. Linear Algebra and its Applications 429(5-6), 1254–1276 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Langville, A., Meyer, C.: Deeper inside pagerank. Internet Mathematics 1(3), 335–380 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Nemhauser, G., Wolsey, L., Fisher, M.: An analysis of approximations for maximizing submodular set functionsI. Mathematical Programming 14(1), 265–294 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Olsen, M.: Maximizing PageRank with New Backlinks. In: Calamoneri, T., Diaz, J. (eds.) Algorithms and Complexity. LNCS, vol. 6078, pp. 37–48. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: Bringing order to the web. Technical Report 1999-66, Stanford InfoLab (November 1999),
  9. 9.
    SEOmoz: Search engine 2009 ranking factors (2009),

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Center for Innovation and Business Development, Institute of Business and TechnologyAarhus UniversityHerningDenmark
  2. 2.School of Information TechnologiesUniversity of SydneyAustralia

Personalised recommendations