We propose a new self-stabilizing 1-maximal matching algorithm which is
and works for any
networks without a cycle of a length of a multiple of 3 under a central
be the numbers of nodes and edges in a graph, respectively. The time complexity of the proposed algorithm is
) moves. Therefore, the complexity is
) moves for trees or rings whose length is not a multiple of 3. That is a significant improvement from the best existing results of
) moves for the same problem setting.