Simplified and Space-Optimal Semi-Streaming (2+epsilon)-Approximate Matching.

In a recent breakthrough, Paz and Schwartzman (SODAu002717) presented a single-pass ($2+epsilon$)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses $O(nlog^2 n)$ bits of space, for any constant $epsilonu003e0$. We present two simplified and more intuitive analyses, for essentially the same algorithm, which also improve the space complexity to the optimal bound of $O(nlog n)$ bits --- this is optimal as the output matching requires $Omega(nlog n)$ bits. Our analyses rely on a simple use of the primal-dual method and a simple accounting method.