We present a simple semi-streaming algorithm for (1-ε) -approximation of bipartite matching in O (\! (n) /ε) passes. This matches the performance of state-of-the-art ε-efficient algorithms -- the ones with much better dependence on ε albeit with some mild dependence on n -- while being considerably simpler. The algorithm relies on a direct application of the multiplicative weight update method with a self-contained primal-dual analysis that can be of independent interest. To show case this, we use the same ideas, alongside standard tools from matching theory, to present an equally simple semi-streaming algorithm for (1-ε) -approximation of weighted matchings in general (not necessarily bipartite) graphs, again in O (\! (n) /ε) passes. 25 pages. This is the TheoretiCS journal version
Sepehr Assadi (Fri,) studied this question.