  A multi-channel MAC seems to be an interesting approach for improving network
throughput by multiplexing transmissions over orthogonal channels. In
particular, Molecular MAC has recently proposed to modify the standard IEEE
802.11 DCF access method to use dynamic channel switching for efficient packet
forwarding over multiple hops. However, this MAC layer requires role and
channel assignment to nodes: some of them use a static channel, while others
dynamically switch to neighbor channels on-demand. To assign roles and
channels, we extend the notion of the Weakly Connected Dominating Set, the
structure already used in clustering. More precisely, we adapt the WCDS
structure and introduce new constraints to define what we call a reversible
WCDS (r-WCDS), which is particularly suitable for wireless mesh networks
operating under Molecular MAC. We propose a divide-and-conquer scheme that
partitions the network into clusters with one leader per cluster solving a MILP
formulation to assign roles in its cluster. By appropriately defining the roles
at the border of clusters, we maintain global connectivity in the r-wcds.
Finally, our simulations show that the performance of the propose scheme is
close to a centralized algorithm.
