Maximum Matching in Turnstile Streams

We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass 2-approximation streaming algorithm can be easily obtained with space O(n logn), where n denotes the number of vertices of the input graph. We show that no such result is possible if edge deletions are allowed, even if space O(n3/2 − δ) is granted, for every δ > 0. Specifically, for every 0 ≤ e ≤ 1, we show that in the one-pass turnstile streaming model, in order to compute a O(n e )-approximation, space Ω(n3/2 − 4e) is required for constant error randomized algorithms, and, up to logarithmic factors, space \(\tilde{\mathrm{O}}( n^{2-2\epsilon} )\) is sufficient.