Tight Bounds for MIS in Multichannel Radio Networks

In [8] an algorithm has been presented that computes a maximal independent set (MIS) withinO(log n/F + log n polyloglogn) rounds in an n-node multichannel radio network with F commu-nication channels. The paper uses a multichannel variant of the standard graph-based radio networkmodel without collision detection and it assumes that the network graph is a polynomially bounded in-dependence graph (BIG), a natural combinatorial generalization of well-known geographic families. Theupper bound of [8] is known to be optimal up to a polyloglog factor.In this paper, we adapt algorithm and analysis to improve the result of [8] in two ways. Mainly, weget rid of the polyloglog factor in the runtime and we thus obtain an asymptotically optimal multichannelradio network MIS algorithm. In addition, our new analysis allows to generalize the class of graphs fromthose with polynomially bounded local independence to graphs where the local independence is boundedby an arbitrary function of the neighborhood radius.