Ignorant vs. Anonymous Recommendations

  • Jara UittoEmail author
  • Roger Wattenhofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


We start with an unknown binary n ×m matrix, where the entries correspond to the preferences of n users on m items. The goal is to find at least one item per user that the user likes, with as few queries as possible. Since there are matrices where any algorithm performs badly without any preliminary knowledge of the input matrix, we reveal an anonymized version of the input matrix to the algorithm in the beginning of the execution. The input matrix is anonymized by shuffling the rows according to a randomly chosen hidden permutation. We observe that this anonymous recommendation problem can be seen as an adaptive variant of the Min Sum Set Cover problem and show that the greedy solution for the original version of the problem provides a constant approximation for the adaptive version.


Recommendation System Greedy Algorithm Preference Vector Recommendation Algorithm Competitive Analysis 
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.


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  1. 1.
    Albers, S.: A Competitive Analysis of the List Update Problem with Lookahead. Theoretical Computer Science 197, 95–109 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alon, N., Awerbuch, B., Azar, Y., Patt-Shamir, B.: Tell Me Who I Am: an Interactive Recommendation System. In: Proceedings of the 18th Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 261–279 (2006)Google Scholar
  3. 3.
    Awerbuch, B., Patt-Shamir, B., Peleg, D., Tuttle, M.R.: Improved Recommendation Systems. In: Proceedings of the 16th Symposium on Discrete Algorithms (SODA), pp. 1174–1183 (2005)Google Scholar
  4. 4.
    Azar, Y., Gamzu, I.: Ranking with Submodular Valuations. In: Proceedings of the 22nd Symposium on Discrete Algorithms (SODA), pp. 1070–1079 (2011)Google Scholar
  5. 5.
    Bar-Noy, A., Bellare, M., Halldórsson, M.M., Shachnai, H., Tamir, T.: On Chromatic Sums and Distributed Resource Allocation. Information and Computation 140(2), 183–202 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bikhchandani, S., de Vries, S., Schummer, J., Vohra, R.: An Ascending Vickrey Auction for Selling Bases of a Matroid. Operations Research 59(2), 400–413 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dean, B., Goemans, M., Vondrák, J.: Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity. Mathematics of Operations Research 33, 945–964 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Drineas, P., Kerenidis, I., Raghavan, P.: Competitive Recommendation Systems. In: Proceedings of the 34th Symposium on Theory of Computing (STOC), pp. 82–90 (2002)Google Scholar
  9. 9.
    Feige, U., Lovász, L., Tetali, P.: Approximating Min Sum Set Cover. Algorithmica 40, 219–234 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Goemans, M.X., Vondrák, J.: Stochastic Covering and Adaptivity. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 532–543. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Goldman, S.A., Schapire, R.E., Rivest, R.L.: Learning Binary Relations and Total Orders. SIAM Journal of Computing 20(3), 245 (1993)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Golovin, D., Krause, A.: Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization. Journal of Artificial Intelligence Research (JAIR) 42, 427–486 (2011)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Grove, E.: Online Bin Packing with Lookahead. In: Proceedings of the 6th Symposium on Discrete Algorithms (SODA), pp. 430–436 (1995)Google Scholar
  14. 14.
    Gupta, A., Nagarajan, V., Ravi, R.: Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 690–701. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Kranton, R., Minehart, D.: A Theory of Buyer-Seller Networks. American Economic Review 91, 485–508 (2001)CrossRefGoogle Scholar
  16. 16.
    Liu, Z., Parthasarathy, S., Ranganathan, A., Yang, H.: Near-Optimal Algorithms for Shared Filter Evaluation in Data Stream Systems. In: Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data, pp. 133–146 (2008)Google Scholar
  17. 17.
    Munagala, K., Babu, S., Motwani, R., Widom, J.: The Pipelined Set Cover Problem. In: Proceedings of the 10th International Conference on Database Theory (ICDT), pp. 83–98 (2005)Google Scholar
  18. 18.
    Nisgav, A., Patt-Shamir, B.: Finding Similar Users in Social Networks: Extended Abstract. In: Proceedings of the 21st Annual Symposium on Parallelism in Algorithms and Architectures, SPAA (2009)Google Scholar
  19. 19.
    Uitto, J., Wattenhofer, R.: On Competitive Recommendations. In: Proceedings of the 24th International Conference on Algorithmic Learning Theory (ALT), pp. 83–97 (2013); (Invited to a special issue of Theoretical Computer Science)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland

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