A Simple $(1-ε)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching

We present a simple semi-streaming algorithm for $(1-ε)$-approximation of bipartite matching in O(log\!(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(log\!(n)/ε) passes. 25 pages. This is the TheoretiCS journal version