Boolean Tensor Decomposition for Conjunctive Queries with Negation

Authors Mahmoud Abo Khamis, Hung Q. Ngo, Dan Olteanu, Dan Suciu

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Author Details

Mahmoud Abo Khamis
  • RelationalAI, Berkeley, USA
Hung Q. Ngo
  • RelationalAI, Berkeley, USA
Dan Olteanu
  • Department of Computer Science, University of Oxford, UK
Dan Suciu
  • Department of Computer Science and Engineering, University of Washington, USA


The authors would like to thank the anonymous reviewers for their suggestions that helped improve the readability of this paper.

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Mahmoud Abo Khamis, Hung Q. Ngo, Dan Olteanu, and Dan Suciu. Boolean Tensor Decomposition for Conjunctive Queries with Negation. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We propose an approach for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the InsideOut and PANDA algorithms for the positive subquery of the input query and is expressed in terms of the fractional hypertree width and the submodular width respectively. Its query complexity depends on the structure of the conjunction of negated relations; in general it is exponential in the number of join variables occurring in negated relations yet it becomes polynomial for several classes of queries. This approach relies on several contributions. We show how to rewrite queries with negation on bounded-degree relations into equivalent conjunctive queries with not-all-equal (NAE) predicates, which are a multi-dimensional analog of disequality (!=). We then generalize the known color-coding technique to conjunctions of NAE predicates and explain it via a Boolean tensor decomposition of conjunctions of NAE predicates. This decomposition can be achieved via a probabilistic construction that can be derandomized efficiently.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query processing and optimization (theory)
  • Information systems → Database query processing
  • color-coding
  • combined complexity
  • negation
  • query evaluation


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