Problem 64: Matchings in the Turnstile Model

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

Consider an unweighted graph on $n$ nodes defined by a stream of edge insertions and deletions. Is it possible to approximate the size of the maximum cardinality matching up to constant factor given a single pass and $o(n^2)$ space? Recall that a factor 2 approximation is easy in $O(n \log n)$ space if there are no edge deletions.