  The bipartite matching problem in the online and streaming settings has
received a lot of attention recently. The classical vertex arrival setting, for
which the celebrated Karp, Vazirani and Vazirani (KVV) algorithm achieves a
$1-1/e$ approximation, is rather well understood: the $1-1/e$ approximation is
optimal in both the online and semi-streaming setting, where the algorithm is
constrained to use $n\cdot \log^{O(1)} n$ space. The more challenging the edge
arrival model has seen significant progress recently in the online algorithms
literature. For the strictly online model (no preemption) approximations better
than trivial factor $1/2$ have been ruled out [Gamlath et al'FOCS'19]. For the
less restrictive online preemptive model a better than $\frac1{1+\ln
2}$-approximation [Epstein et al'STACS'12] and even a better than
$(2-\sqrt{2})$-approximation[Huang et al'SODA'19] have been ruled out.
  The recent hardness results for online preemptive matching in the edge
arrival model are based on the idea of stringing together multiple copies of a
KVV hard instance using edge arrivals. In this paper, we show how to implement
such constructions using ideas developed in the literature on Ruzsa-Szemer\'edi
graphs. As a result, we show that any single pass streaming algorithm that
approximates the maximum matching in a bipartite graph with $n$ vertices to a
factor better than $\frac1{1+\ln 2}\approx 0.59$ requires
$n^{1+\Omega(1/\log\log n)}\gg n \log^{O(1)} n$ space. This gives the first
separation between the classical one sided vertex arrival setting and the edge
arrival setting in the semi-streaming model.
