The Mann et al. self-stabilizing 2/3−approximation matching algorithm is sub-exponential.
Johanne Cohen, Khaled Maâmra, George Manoussakis, Laurence Pilard · HAL (Le Centre pour la Communication Scientifique Directe) · 2016
Mann et al. [11] designed the first algorithm computing a maximal matching that is a 2/3- approximation of the maximum matching in 2^O(n) moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm: this algorithm can stabilize after at most Ω(2^{sqrt(n)} moves under the central daemon.