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We present TRI\`EST, a suite of one-pass streaming algorithms to computeunbiased, low-variance, high-quality approximations of the global and local(i.e., incident to each vertex) number of triangles in a fully-dynamic graphrepresented as an adversarial stream of edge insertions and deletions. Ouralgorithms use reservoir sampling and its variants to exploit theuser-specified memory space at all times. This is in contrast with previousapproaches which use hard-to-choose parameters (e.g., a fixed samplingprobability) and offer no guarantees on the amount of memory they will use. Weshow a full analysis of the variance of the estimations and novel concentrationbounds for these quantities. Our experimental results on very large graphs showthat TRI\`EST outperforms state-of-the-art approaches in accuracy and exhibitsa small update time.

TRI\`EST: Counting Local and Global Triangles in Fully-dynamic Streams with Fixed Memory Size