Simplified and Space-Optimal Semi-Streaming (2+epsilon)-Approximate Matching
Mohsen Ghaffari, David Wajc · arXiv (Cornell University) · 2019
In a recent breakthrough, Paz and Schwartzman (SODA'17) presented a single-pass (2+epsilon)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses O(n log^2 n) bits of space, for any constant epsilon>0. We present a simplified and more intuitive primal-dual analysis, for essentially the same algorithm, which also improves the space complexity to the optimal bound of O(n log n) bits - this is optimal as the output matching requires Omega(n log n) bits.