Polynomial self-stabilizing algorithm and proof for a 2/3-approximation of a maximum matching

TL;DR

This paper introduces the first polynomial self-stabilizing algorithm that efficiently approximates a maximum matching within a factor of 2/3 in general graphs, improving on previous algorithms with sub-exponential complexity.

Contribution

It presents a novel polynomial-time self-stabilizing algorithm for a 2/3-approximation of maximum matching, building upon and adapting prior work with improved complexity.

Findings

Algorithm runs in O(n^3) moves under the distributed adversarial daemon.

Requires only one additional boolean variable, maintaining constant memory per node.

Achieves a 2/3-approximation of maximum matching in polynomial time.

Abstract

We present the first polynomial self-stabilizing algorithm for finding a $\frac23$-approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne \emph{et al.} \cite{ManneMPT11} and has a sub-exponential time complexity under the distributed adversarial daemon \cite{Coor}. Our new algorithm is an adaptation of the Manne \emph{et al.} algorithm and works under the same daemon, but with a time complexity in $O(n^3)$ moves. Moreover, our algorithm only needs one more boolean variable than the previous one, thus as in the Manne \emph{et al.} algorithm, it only requires a constant amount of memory space (three identifiers and $two$ booleans per node).