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(n^{3/2 − δ}) is granted, for every δ > 0. Specifically, for every 0 ≤ ε ≤ 1, we show that in the one-pass turnstile streaming model, in order to compute a O(n ^ε )-approximation, space Ω(n^{3/2 − 4ε}) is required for constant error randomized algorithms, and, up to logarithmic factors, space O~(n2−2ϵ) is sufficient.

Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest.