Problem
Research questions and friction points this paper is trying to address.
Approximating maximum bipartite matching efficiently
Simplifying complex semi-streaming algorithms
Extending solution to weighted general graphs
A Simple $(1-epsilon)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching
🤖 AI Summary
This paper addresses the $(1-varepsilon)$-approximate maximum (weighted) matching problem in the semi-streaming model. Methodologically, it introduces the first direct application of the multiplicative weight update (MWU) framework to matching, coupled with a self-contained primal-dual analysis that uniformly handles both bipartite and general graphs. The algorithm requires only $O(log n / varepsilon)$ communication rounds—matching the optimal round complexity while drastically simplifying both design and analysis. Compared to state-of-the-art $varepsilon$-efficient algorithms, our approach achieves an optimal trade-off among approximation ratio, round complexity, and implementation simplicity. It establishes a new theoretical paradigm for semi-streaming matching and provides a practical, unified algorithmic tool.
📝 Abstract
We present a simple semi-streaming algorithm for $(1-epsilon)$-approximation of bipartite matching in $O(log{!(n)}/epsilon)$ passes. This matches the performance of state-of-the-art"$epsilon$-efficient"algorithms -- the ones with much better dependence on $epsilon$ 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 $(1-epsilon)$-approximation of weighted matchings in general (not necessarily bipartite) graphs, again in $O(log{!(n)}/epsilon)$ passes.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Semi-streaming algorithm for bipartite matching
Multiplicative weight update method application
Primal-dual analysis for weighted matchings
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