skip to main content
10.1145/2213556.2213592acmconferencesArticle/Chapter ViewAbstractPublication PagespodsConference Proceedingsconference-collections
research-article

On the complexity of package recommendation problems

Published: 21 May 2012 Publication 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.
[2]
G. Adomavicius and A. Tuzhilin. Multidimensional recommender systems: A data warehousing approach. In WELCOM, 2001.
[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.
[4]
S. Amer-Yahia. Recommendation projects at Yahoo! IEEE Data Eng. Bull., 34(2):69--77, 2011.
[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.
[6]
A. Angel, S. Chaudhuri, G. Das, and N. Koudas. Ranking objects based on relationships and fixed associations. In EDBT, 2009.
[7]
A. Brodsky, S. Henshaw, and J. Whittle. CARD: A decision-guidance framework and application for recommending composite alternatives. In RecSys, 2008.
[8]
S. Chaudhuri. Generalization and a framework for query modification. In ICDE, 1990.
[9]
S. Chaudhuri and M. Y. Vardi. On the equivalence of recursive and nonrecursive Datalog programs. JCSS, 54(1):61--78, 1997.
[10]
S. Cohen and Y. Sagiv. An incremental algorithm for computing ranked full disjunctions. JCSS, 73(4):648--668, 2007.
[11]
A. Durand, M. Hermann, and P. G. Kolaitis. Subtractive reductions and complete problems for counting complexity classes. TCS, 340(3):496--513, 2005.
[12]
R. Fagin, A. Lotem, and M. Naor. Optimal aggregation algorithms for middleware. JCSS, 66(4):614--656, 2003.
[13]
T. Gaasterland and J. Lobo. Qualifying answers according to user needs and preferences. Fundam. Inform., 32(2):121--137, 1997.
[14]
K. Golenberg, B. Kimelfeld, and Y. Sagiv. Optimizing and parallelizing ranked enumeration. PVLDB, 4(11):1028--1039, 2011.
[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.
[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.
[17]
A. Kadlag, A. V. Wanjari, J. Freire, and J. R. Haritsa. Supporting exploratory queries in databases. In DASFAA, 2004.
[18]
N. Koudas, C. Li, A. K. H. Tung, and R. Vernica. Relaxing join and selection queries. In VLDB, 2006.
[19]
G. Koutrika, B. Bercovitz, and H. Garcia-Molina. FlexRecs: expressing and combining flexible recommendations. In SIGMOD, 2009.
[20]
M. W. Krentel. Generalizations of Opt P to the polynomial hierarchy. TCS, 97(2):183--198, 1992.
[21]
R. E. Ladner. Polynomial space counting problems. SIAM J. Comput., 18(6):1087--1097, 1989.
[22]
T. Lappas, K. Liu, and E. Terzi. Finding a team of experts in social networks. In KDD, 2009.
[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.
[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.
[25]
C. H. Papadimitriou. Computational Complexity. AW, 1994.
[26]
A. G. Parameswaran, H. Garcia-Molina, and J. D. Ullman. Evaluating, combining and generalizing recommendations with prerequisites. In CIKM, 2010.
[27]
A. G. Parameswaran, P. Venetis, and H. Garcia-Molina. Recommendation systems with complex constraints: A course recommendation perspective. TOIS, 29(4), 2011.
[28]
K. Schnaitter and N. Polyzotis. Evaluating rank joins with optimal cost. In PODS, 2008.
[29]
K. Stefanidis, G. Koutrika, and E. Pitoura. A survey on representation, composition and application of preferences in database systems. TODS, 36(3), 2011.
[30]
L. J. Stockmeyer. The polynomial-time hierarchy. TCS, 3(1):1--22, 1976.
[31]
L. Valiant. The complexity of computing the permanent. TCS, 8(2):189--201, 1979.
[32]
M. Y. Vardi. The complexity of relational query languages. In STOC, 1982.
[33]
M. Wooldridge and P. E. Dunne. On the computational complexity of qualitative coalitional games. Artif. Intell., 158(1):27--73, 2004.
[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.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

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
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 May 2012

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. complexity
  2. query relaxation
  3. recommendation problems

Qualifiers

  • Research-article

Conference

SIGMOD/PODS '12
Sponsor:

Acceptance Rates

PODS '12 Paper Acceptance Rate 26 of 101 submissions, 26%;
Overall Acceptance Rate 642 of 2,707 submissions, 24%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)15
  • Downloads (Last 6 weeks)0
Reflects downloads up to 01 Jan 2025

Other Metrics

Citations

Cited By

View all

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media