The Manne et al. self-stabilizing 2/3-approximation matching algorithm is sub-exponential

TL;DR

This paper demonstrates that the Manne et al. 2/3-approximation matching algorithm, previously thought to have polynomial complexity, can actually have sub-exponential execution time, challenging assumptions about its efficiency.

Contribution

The paper provides the first example of sub-exponential execution of the Manne et al. matching algorithm, establishing new complexity bounds.

Findings

The algorithm can run in sub-exponential time.

It challenges previous beliefs about the algorithm's polynomial complexity.

Provides insights into the algorithm's practical performance.

Abstract

Manne et al. designed the first algorithm computing a maximal matching that is a 2/3 -approximation of the maximum matching in $O(^2n)$ moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm.