Improved Approximation Guarantee for Max Sum Diversification with Parameterised Triangle Inequality

  • Marcin Sydow
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8502)


We present improved 2/α approximation guarantee for the problem of selecting diverse set of p items when its formulation is based on Max Sum Facility Dispersion problem and the underlying dissimilarity measure satisfies parameterised triangle inequality with parameter α.

Diversity-aware approach is gaining interest in many important applications such as web search, recommendation, database querying or summarisation, especially in the context of ambiguous user query or unknown user profile.

In addition, we make some observations on the applicability of these results in practical computations on real data and link to important recent applications in the result diversification problem in web search and semantic graph summarisation. The results apply to both relaxed and strengthen variants of the triangle inequality.


diversity max sum facility dispersion approximation algorithms parameterised triangle inequality 


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  1. 1.
    Andreae, T., Bandelt, H.-J.: Performance guarantees for approximation algorithms depending on parametrized triangle inequalities. SIAM Journal of Discrete Mathematics 8, 1–16 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Fagin, R., Stockmeyer, L.: Relaxing the triangle inequality in pattern matching. Int. J. Comput. Vision 30(3), 219–231 (1998)CrossRefGoogle Scholar
  3. 3.
    Gollapudi, S., Sharma, A.: An axiomatic approach for result diversification. In: Proceedings of the 18th International Conference on World Wide Web, WWW 2009, pp. 381–390. ACM, New York (2009)CrossRefGoogle Scholar
  4. 4.
    Gonzalez, T.F.: Handbook of approx. algorithms and metaheuristics. CRC Press (2007)Google Scholar
  5. 5.
    Hassin, R., Rubinstein, S., Tamir, A.: Approximation algorithms for maximum dispersion. Oper. Res. Lett. 21(3), 133–137 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Kosiński, W., Kuśmierczyk, T., Rembelski, P., Sydow, M.: Application of ant-colony optimisation to compute diversified entity summarisation on semantic knowledge graphs. In: Proc. of International IEEE AAIA 2013/FedCSIS Conference, Annals of Computer Science and Information Systems, vol. 1, pp. 69–76 (2013)Google Scholar
  7. 7.
    Ravi, S.S., Rosenkrantz, D.J., Tayi, G.K.: Heuristic and special case algorithms for dispersion problems. Operations Research 42(2), 299–310 (1994)CrossRefzbMATHGoogle Scholar
  8. 8.
    Sydow, M., Pikula, M., Schenkel, R.: The notion of diversity in graphical entity summarisation on semantic knowledge graphs. Journal of Intelligent Information Systems 41, 109–149 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marcin Sydow
    • 1
    • 2
  1. 1.Institute of Computer SciencePolish Academy of SciencesWarsawPoland
  2. 2.Web Mining LabPolish-Japanese Institute of Information TechnologyWarsawPoland

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