An Optimal Algorithm for the Distinct Elements Problem

We give the first optimal algorithm for estimating the number of distinct elements in a data stream, closing a long line of theoretical research on this problem begun by Flajolet and Martin in their seminal paper in FOCS 1983. This problem has applications to query optimization, Internet routing, network topology, and data mining. For a stream of indices in {1,...,n}, our algorithm computes a \((1 \pm \epsilon)\)-approximation using an optimal \(O(1/\epsilon^{-2} + log(n))\) bits of space with 2/3 success probability, where \(0<\epsilon