Problem 64: Matchings in the Turnstile Model

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Suggested by Andrew McGregor
Source Bertinoro 2014
Short link https://sublinear.info/64

Suppose we are in a turnstile model for graph streaming: this means that the stream consists of a sequence of edge insertions and deletions (with no edge being deleted before it's inserted). In this setting, can we design an algorithm for computing a matching that takes space $o(n^2)$ and gets a constant-factor approximation (or better)?