Theory of Computing Systems

, Volume 61, Issue 1, pp 2–30

Answering Conjunctive Queries with Inequalities

  • Paraschos Koutris
  • Tova Milo
  • Sudeepa Roy
  • Dan Suciu
Article

DOI: 10.1007/s00224-016-9684-2

Cite this article as:
Koutris, P., Milo, T., Roy, S. et al. Theory Comput Syst (2017) 61: 2. doi:10.1007/s00224-016-9684-2
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Abstract

In this paper, we study the complexity of answering conjunctive queries (CQ) with inequalities (≠). In particular, we are interested in comparing the complexity of the query with and without inequalities. The main contribution of our work is a novel combinatorial technique that enables us to use any Select-Project-Join query plan for a given CQ without inequalities in answering the CQ with inequalities, with an additional factor in running time that only depends on the query. The key idea is to define a new projection operator, which keeps a small representation (independent of the size of the database) of the set of input tuples that map to each tuple in the output of the projection; this representation is used to evaluate all the inequalities in the query. Second, we generalize a result by Papadimitriou and Yannakakis (1997) and give an alternative algorithm based on the color-coding technique (2008) to evaluate a CQ with inequalities by using an algorithm for the CQ without inequalities. Third, we investigate the structure of the query graph, inequality graph, and the augmented query graph with inequalities, and show that even if the query and the inequality graphs have bounded treewidth, the augmented graph not only can have an unbounded treewidth but can also be NP-hard to evaluate. Further, we illustrate classes of queries and inequalities where the augmented graphs have unbounded treewidth, but the CQ with inequalities can be evaluated in poly-time. Finally, we give necessary properties and sufficient properties that allow a class of CQs to have poly-time combined complexity with respect to any inequality pattern. We also illustrate classes of queries where our query-plan-based technique outperforms the alternative approaches discussed in the paper.

Keywords

Query evaluation Conjunctive query Inequality Treewidth 

Funding information

Funder NameGrant NumberFunding Note
National Science Foundation (US)
  • IIS-1247469
National Science Foundation (US)
  • IIS-0911036
European Research Council (BE)
  • MoDas, agreement 291071
Ministry of Science and Technology, Israel (IL)

    Copyright information

    © Springer Science+Business Media New York 2016

    Authors and Affiliations

    • Paraschos Koutris
      • 1
    • Tova Milo
      • 2
    • Sudeepa Roy
      • 1
    • Dan Suciu
      • 1
    1. 1.University of WashingtonSeattleUSA
    2. 2.Tel Aviv UniversityTel AvivIsrael

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