# A $(2+\epsilon)$-Approximation for Maximum Weight Matching in the Semi-Streaming Model

## TL;DR

This paper introduces a simple deterministic algorithm that achieves a near-optimal approximation for maximum weight matching in the semi-streaming model, improving the approximation ratio significantly with efficient space usage.

## Contribution

It presents the first deterministic single-pass $(2+ ext{epsilon})$-approximation algorithm for maximum weight matching in semi-streaming, utilizing a novel variation of the local-ratio theorem.

## Key findings

- Achieves a $(2+ ext{epsilon})$-approximation ratio.
- Uses $O(n ext{log}^2 n)$ bits of space.
- Improves upon the previous $(4+ ext{epsilon})$ approximation.

## Abstract

We present a simple deterministic single-pass $(2+\epsilon)$-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves upon the currently best known approximation ratio of $(4+\epsilon)$. Our algorithm uses $O(n\log^2 n)$ bits of space for constant values of $\epsilon$. It relies on a variation of the local-ratio theorem, which may be of use for other algorithms in the semi-streaming model as well.