Counting Triangles under Updates in Worst-Case Optimal Time

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 update maintenance, which is suboptimal. Our approach can also be used to count all triangles in a static database in the worst-case optimal time to enumerate the triangles. This is a joint work with Hung Q. Ngo, Milos Nikolic, Dan Olteanu, and Haozhe Zhang and will appear in ICDT 2019.

Authors

• Ahmet Kara

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