  We consider the problem of approximating a maximum weighted matching, when
the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming
fashion. We analyze a variant of the previously best-known
$(4+\epsilon)$-approximation algorithm due to Crouch and Stubbs (APPROX, 2014),
and prove their conjecture that it achieves a tight approximation factor of
$3.5+\epsilon$.
  The algorithm splits the stream into substreams on which it runs a greedy
maximum matching algorithm. At the end of the stream, the selected edges are
given as input to an optimal maximum weighted matching algorithm. To analyze
the approximation guarantee, we develop a novel charging argument in which we
decompose the edges of a maximum weighted matching of $G$ into a few natural
classes, and then charge them separately to the edges of the matching output by
our algorithm.
