A Simplification of the MV Matching Algorithm and its Proof

TL;DR

This paper simplifies the proof of correctness for the Micali-Vazirani maximum matching algorithm, making it more accessible while also aiding in the simplification of the algorithm itself.

Contribution

It provides a clearer, more straightforward proof of the Micali-Vazirani algorithm's correctness and introduces graph-theoretic tools to simplify the algorithm.

Findings

Proof of correctness is now more accessible and simpler

Graph-theoretic machinery aids in simplifying the algorithm

Maintains the algorithm's status as the most efficient known for maximum matching

Abstract

For all practical purposes, the Micali-Vazirani general graph maximum matching algorithm is still the most efficient known algorithm for the problem. The purpose of this paper is to provide a complete proof of correctness of the algorithm in the simplest possible terms; graph-theoretic machinery developed for this purpose also helps simplify the algorithm.