Enumeration and Updates for Conjunctive Linear Algebra Queries Through Expressibility

Authors Thomas Muñoz Serrano , Cristian Riveros , Stijn Vansummeren

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Thomas Muñoz Serrano
  • UHasselt, Data Science Institute, Diepenbeek, Belgium
Cristian Riveros
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile
Stijn Vansummeren
  • UHasselt, Data Science Institute, Diepenbeek, Belgium

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Thomas Muñoz Serrano, Cristian Riveros, and Stijn Vansummeren. Enumeration and Updates for Conjunctive Linear Algebra Queries Through Expressibility. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular, in recent years close connections have been established between linear algebra programs and relational algebra that allow transferring optimization techniques of the latter to the former. In this paper, we ask ourselves which linear algebra programs in MATLANG correspond to the free-connex and q-hierarchical fragments of conjunctive first-order logic. Both fragments have desirable query processing properties: free-connex conjunctive queries support constant-delay enumeration after a linear-time preprocessing phase, and q-hierarchical conjunctive queries further allow constant-time updates. By characterizing the corresponding fragments of MATLANG, we hence identify the fragments of linear algebra programs that one can evaluate with constant-delay enumeration after linear-time preprocessing and with constant-time updates. To derive our results, we improve and generalize previous correspondences between MATLANG and relational algebra evaluated over semiring-annotated relations. In addition, we identify properties on semirings that allow to generalize the complexity bounds for free-connex and q-hierarchical conjunctive queries from Boolean annotations to general semirings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database theory
  • Query evaluation
  • conjunctive queries
  • linear algebra
  • enumeration algorithms


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