License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICDT.2019.4
URN: urn:nbn:de:0030-drops-103068
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10306/
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Kara, Ahmet ; Ngo, Hung Q. ; Nikolic, Milos ; Olteanu, Dan ; Zhang, Haozhe

Counting Triangles under Updates in Worst-Case Optimal Time

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LIPIcs-ICDT-2019-4.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{kara_et_al:LIPIcs:2019:10306,
  author =	{Ahmet Kara and Hung Q. Ngo and Milos Nikolic and Dan Olteanu and Haozhe Zhang},
  title =	{{Counting Triangles under Updates in Worst-Case Optimal Time}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Pablo Barcelo and Marco Calautti},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10306},
  doi =		{10.4230/LIPIcs.ICDT.2019.4},
  annote =	{Keywords: incremental view maintenance, amortized analysis, data skew}
}

Keywords: incremental view maintenance, amortized analysis, data skew
Collection: 22nd International Conference on Database Theory (ICDT 2019)
Issue Date: 2019
Date of publication: 19.03.2019

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