A Simple Analysis of Ranking in General Graphs

TL;DR

This paper offers a straightforward combinatorial analysis of the Ranking algorithm, showing it achieves slightly better than 50% approximation for maximum matching in general graphs.

Contribution

It provides a simple, improved analysis of the Ranking algorithm's performance on general graphs, achieving a $(1/2 + c)$ approximation with $c \\geq 0.005$.

Findings

Ranking algorithm achieves at least 55.5% approximation in general graphs.

The analysis simplifies understanding of the algorithm's effectiveness.

Improves previous bounds on the algorithm's performance.

Abstract

We provide a simple combinatorial analysis of the Ranking algorithm, originally introduced in the seminal work by Karp, Vazirani, and Vazirani [KVV90], demonstrating that it achieves a $(1/2 + c)$-approximate matching for general graphs for $c \geq 0.005$.