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.