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Counting Triangles under Updates in Worst-Case Optimal Time

Authors Ahmet Kara, Hung Q. Ngo, Milos Nikolic, Dan Olteanu, Haozhe Zhang

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Author Details

Ahmet Kara
  • Department of Computer Science, University of Oxford, Oxford, UK
Hung Q. Ngo
  • RelationalAI, Inc., Berkeley, CA, USA
Milos Nikolic
  • School of Informatics, University of Edinburgh, Edinburgh, UK
Dan Olteanu
  • Department of Computer Science, University of Oxford, Oxford, UK
Haozhe Zhang
  • Department of Computer Science, University of Oxford, Oxford, UK

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 682588. Kara acknowledges funding from Fondation Wiener Anspach.

Acknowledgements

Olteanu would like to thank Nicole Schweikardt for the connection between the Online Matrix-Vector Multiplication conjecture and the triangle query.

Cite As Get BibTex

Ahmet Kara, Hung Q. Ngo, Milos Nikolic, Dan Olteanu, and Haozhe Zhang. Counting Triangles under Updates in Worst-Case Optimal Time. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICDT.2019.4

Abstract

We consider the problem of incrementally maintaining the triangle count query under single-tuple updates to the input relations. We introduce an approach that exhibits a space-time tradeoff such that the space-time product is quadratic in the size of the input database and the update time can be as low as the square root of this size. This lowest update time is worst-case optimal conditioned on the Online Matrix-Vector Multiplication conjecture.
The classical and factorized incremental view maintenance approaches are recovered as special cases of our approach within the space-time tradeoff. In particular, they require linear-time maintenance under updates, which is suboptimal. Our approach can also count all triangles in a static database in the worst-case optimal time needed for enumerating them.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query processing and optimization (theory)
  • Information systems → Database views
  • Information systems → Data streams
Keywords
  • incremental view maintenance
  • amortized analysis
  • data skew

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References

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