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On the complexity of package recommendation problems

Published:21 May 2012Publication History

ABSTRACT

Recommendation systems aim to recommend items that are likely to be of interest to users. This paper investigates several issues fundamental to such systems.

  • We model recommendation systems for packages of items. We use queries to specify multi-criteria for item selections and express compatibility constraints on items in a package, and use functions to compute the cost and usefulness of items to a user.

  • We study recommendations of points of interest, to suggest top-k packages. We also investigate recommendations of top-k items, as a special case. In addition, when sensible suggestions cannot be found, we propose query relaxation recommendations to help users revise their selection criteria, or adjustment recommendations to guide vendors to modify their item collections.

  • We identify several problems, to decide whether a set of packages makes a top-k recommendation, whether a rating bound is maximum for selecting top-k packages, whether we can relax the selection query to find packages that users want, and whether we can update a bounded number of items such that the users' requirements can be satisfied. We also study function problems for computing top-k packages, and counting problems to find how many packages meet the user's criteria.

  • We establish the upper and lower bounds of these problems, all matching, for combined and data complexity. These results reveal the impact of variable sizes of packages, the presence of compatibility constraints, as well as a variety of query languages for specifying selection criteria and compatibility constraints, on the analyses of these problems.

References

  1. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. G. Adomavicius and A. Tuzhilin. Multidimensional recommender systems: A data warehousing approach. In WELCOM, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. G. Adomavicius and A. Tuzhilin. Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions. TKDE, 17(6):734--749, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. S. Amer-Yahia. Recommendation projects at Yahoo! IEEE Data Eng. Bull., 34(2):69--77, 2011.Google ScholarGoogle Scholar
  5. S. Amer-Yahia, S. B. Roy, A. Chawla, G. Das, and C. Yu. Group recommendation: Semantics and efficiency. PVLDB, 2(1):754--765, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. A. Angel, S. Chaudhuri, G. Das, and N. Koudas. Ranking objects based on relationships and fixed associations. In EDBT, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. A. Brodsky, S. Henshaw, and J. Whittle. CARD: A decision-guidance framework and application for recommending composite alternatives. In RecSys, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. S. Chaudhuri. Generalization and a framework for query modification. In ICDE, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. S. Chaudhuri and M. Y. Vardi. On the equivalence of recursive and nonrecursive Datalog programs. JCSS, 54(1):61--78, 1997.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. S. Cohen and Y. Sagiv. An incremental algorithm for computing ranked full disjunctions. JCSS, 73(4):648--668, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. A. Durand, M. Hermann, and P. G. Kolaitis. Subtractive reductions and complete problems for counting complexity classes. TCS, 340(3):496--513, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. R. Fagin, A. Lotem, and M. Naor. Optimal aggregation algorithms for middleware. JCSS, 66(4):614--656, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. T. Gaasterland and J. Lobo. Qualifying answers according to user needs and preferences. Fundam. Inform., 32(2):121--137, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. K. Golenberg, B. Kimelfeld, and Y. Sagiv. Optimizing and parallelizing ranked enumeration. PVLDB, 4(11):1028--1039, 2011.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. L. A. Hemaspaandra and H. Vollmer. The satanic notations: counting classes beyond #P and other definitional adventures. SIGACT News, 26(1):2--13, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. I. F. Ilyas, G. Beskales, and M. A. Soliman. A survey of top-k query processing techniques in relational database systems. ACM Comput. Surv., 40(4):11:1--11:58, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. A. Kadlag, A. V. Wanjari, J. Freire, and J. R. Haritsa. Supporting exploratory queries in databases. In DASFAA, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  18. N. Koudas, C. Li, A. K. H. Tung, and R. Vernica. Relaxing join and selection queries. In VLDB, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. G. Koutrika, B. Bercovitz, and H. Garcia-Molina. FlexRecs: expressing and combining flexible recommendations. In SIGMOD, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. M. W. Krentel. Generalizations of Opt P to the polynomial hierarchy. TCS, 97(2):183--198, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. R. E. Ladner. Polynomial space counting problems. SIAM J. Comput., 18(6):1087--1097, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. T. Lappas, K. Liu, and E. Terzi. Finding a team of experts in social networks. In KDD, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. C. Li, M. A. Soliman, K. C.-C. Chang, and I. F. Ilyas. RankSQL: supporting ranking queries in relational database management systems. In VLDB, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. A. Natsev, Y.-C. Chang, J. R. Smith, C.-S. Li, and J. S. Vitter. Supporting incremental join queries on ranked inputs. In VLDB, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. C. H. Papadimitriou. Computational Complexity. AW, 1994.Google ScholarGoogle Scholar
  26. A. G. Parameswaran, H. Garcia-Molina, and J. D. Ullman. Evaluating, combining and generalizing recommendations with prerequisites. In CIKM, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. A. G. Parameswaran, P. Venetis, and H. Garcia-Molina. Recommendation systems with complex constraints: A course recommendation perspective. TOIS, 29(4), 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. K. Schnaitter and N. Polyzotis. Evaluating rank joins with optimal cost. In PODS, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. K. Stefanidis, G. Koutrika, and E. Pitoura. A survey on representation, composition and application of preferences in database systems. TODS, 36(3), 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. L. J. Stockmeyer. The polynomial-time hierarchy. TCS, 3(1):1--22, 1976.Google ScholarGoogle ScholarCross RefCross Ref
  31. L. Valiant. The complexity of computing the permanent. TCS, 8(2):189--201, 1979.Google ScholarGoogle ScholarCross RefCross Ref
  32. M. Y. Vardi. The complexity of relational query languages. In STOC, 1982. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. M. Wooldridge and P. E. Dunne. On the computational complexity of qualitative coalitional games. Artif. Intell., 158(1):27--73, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. M. Xie, L. V. S. Lakshmanan, and P. T. Wood. Breaking out of the box of recommendations: from items to packages. In RecSys, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library

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        • Published in

          cover image ACM Conferences
          PODS '12: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems
          May 2012
          332 pages
          ISBN:9781450312486
          DOI:10.1145/2213556

          Copyright © 2012 ACM

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 21 May 2012

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