Counting Triangles under Updates in Worst-Case Optimal Time

We consider the problem of incrementally maintaining the triangle count query under single-tuple updates to the input relations.

Authors: Ahmet Kara, Hung Q. Ngo, Milos Nikolic, Dan Olteanu, Haozhe Zhang. 2019.

In Proceedings of the 22nd International Conference on Database Theory (ICDT ‘19). (Best Paper Award).

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.

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