On the complexity of query result diversification

  • Authors:

  • Ting Deng;Wenfei Fan

  • Affiliations:

  • Big Data Research Center and SKLSDE Lab, Beihang University;School of Informatics, University of Edinburgh and Big Data Research Center and SKLSDE Lab, Beihang University

  • Venue:
  • Proceedings of the VLDB Endowment
  • Year:
  • 2013

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Abstract

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases.