Counting triangles under updates in worst-case optimal time

Conference item

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.

Authors: Kara, A; Ngo, H; Nikolic, M; Olteanu, D; Zhang, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Schloss Dagstuhl
• Host title: 22nd International Conference on Database Theory (ICDT 2019)
• Journal: 22nd International Conference on Database Theory
• Volume: 127
• Pages: 4:1–4:18
• Series: Leibniz International Proceedings in Informatics
• Publication date: 2019-03-19
• Acceptance date: 2018-05-28
• DOI: 10.4230/LIPIcs.ICDT.2019.4
• ISSN: 1868-8969
• ISBN: 9783959771016
• Keywords: incremental view maintenance; amortized analysis; data skew