Abstract
We are given an unknown binary matrix, where the entries correspond to preferences of users on items. We want to find at least one 1-entry in each row with a minimum number of queries. The number of queries needed heavily depends on the input matrix and a straightforward competitive analysis yields bad results for any online algorithm. Therefore, we analyze our algorithm against a weaker offline algorithm that is given the number of users and a probability distribution according to which the preferences of the users are chosen. We show that our algorithm has an \(\mathcal{O}(\sqrt{n} \log^2 n)\) overhead in comparison to the weaker offline solution. Furthermore, we show that the corresponding overhead for any online algorithm is \(\Omega(\sqrt{n})\), which shows that the performance of our algorithm is within an \(\mathcal{O}(\log^2 n)\) multiplicative factor from optimal.
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References
Albers, S.: A Competitive Analysis of the List Update Problem with Lookahead. Theoretical Computer Science 197, 95–109 (1998)
Alon, N., Awerbuch, B., Azar, Y., Patt-Shamir, B.: Tell Me Who I Am: An Interactive Recommendation System. In: 18th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA (2006)
Awerbuch, B., Patt-Shamir, B., Peleg, D., Tuttle, M.: Collaboration of Untrusting Peers with Changing Interests. In: Proceedings of the 5th ACM Conference on Electronic Commerce (2004)
Awerbuch, B., Patt-Shamir, B., Peleg, D., Tuttle, M.R.: Improved Recommendation Systems. In: 16th ACM-SIAM Symposium on Discrete Algorithms (SODA) (2005)
Azar, Y., Gamzu, I.: Ranking with Submodular Valuations. In: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1070–1079 (2011)
Babu, S., Motwani, R., Munagala, K., Nishizawa, I., Widom, J.: Adaptive Ordering of Pipelined Stream Filters. In: ACM SIGMOD International Conference on Management of Data (2004)
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)
Dean, B., Goemans, M., Vondrák, J.: Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity. Mathematics of Operations Research 33, 945–964 (2008)
Drineas, P., Kerenidis, I., Raghavan, P.: Competitive Recommendation Systems. In: 34th ACM Symposium on Theory of Computing (STOC) (2002)
Feige, U., Lovász, L., Tetali, P.: Approximating Min Sum Set Cover. Algorithmica 40, 219–234 (2004)
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)
Sally, A., Goldman, R.E.: Schapire, and Ronald L. Rivest. Learning Binary Relations and Total Orders. SIAM Journal of Computing 20(3), 245–271 (1993)
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)
Grove, E.: Online Bin Packing with Lookahead. In: Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete algorithms (1995)
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)
Kaplan, H., Kushilevitz, E., Mansour, Y.: Learning with Attribute Costs. In: 37th ACM Symposium on Theory of Computing (STOC) (2005)
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 (2008)
Munagala, K., Babu, S., Motwani, R., Widom, J.: The Pipelined Set Cover Problem. In: Eiter, T., Libkin, L. (eds.) ICDT 2005. LNCS, vol. 3363, pp. 83–98. Springer, Heidelberg (2005)
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Uitto, J., Wattenhofer, R. (2013). On Competitive Recommendations. In: Jain, S., Munos, R., Stephan, F., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2013. Lecture Notes in Computer Science(), vol 8139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40935-6_7
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DOI: https://doi.org/10.1007/978-3-642-40935-6_7
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