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Linear Programs with Conjunctive Queries

Authors Florent Capelli, Nicolas Crosetti, Joachim Niehren, Jan Ramon

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Author Details

Florent Capelli
  • Univ. Lille, Inria, CNRS, UMR 9189 - CRIStAL, F-59000 Lille, France
Nicolas Crosetti
  • Univ. Lille, Inria, CNRS, UMR 9189 - CRIStAL, F-59000 Lille, France
Joachim Niehren
  • Univ. Lille, Inria, CNRS, UMR 9189 - CRIStAL, F-59000 Lille, France
Jan Ramon
  • Univ. Lille, Inria, CNRS, UMR 9189 - CRIStAL, F-59000 Lille, France

Funding

This work was partially supported by the French Agence Nationale de la Recherche, AGGREG project reference ANR-14-CE25-0017-01, Headwork project reference ANR-16-CE23-0015 and by a grant of the Conseil Régional Hauts-de-France. The project DATA, Ministère de l'Enseignement Supérieur et de la Recherche, Région Nord-Pas de Calais and European Regional Development Fund (FEDER) are acknowledged for supporting and funding this work.

Acknowledgements

We also thank Sylvain Salvati, Sophie Tison and Yuyi Wang for fruitful discussions and anonymous reviewers of a previous version of this paper for their helpful comments.

Cite AsGet BibTex

Florent Capelli, Nicolas Crosetti, Joachim Niehren, and Jan Ramon. Linear Programs with Conjunctive Queries. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICDT.2022.5

Abstract

In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The naive approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s-measure of patterns in graphs as needed for data mining.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and databases
Keywords
  • Database queries
  • linear programming
  • hypergraph decomposition

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