Channel Dependent Interference and Decentralized Colouring

We consider channel allocation to mitigate interference between wireless LANs. The channel allocation task is often formulated in the literature as finding a proper colouring of a single graph. We show that the interference between WLANs can be channel dependent in which case a different conflict graph is associated with each channel. Channel allocation then corresponds to a multi-graph colouring problem. This potentially has profound implications as the behaviour of many proposed colouring-based algorithms for channel allocation is unclear in a multi-graph context. We prove that a recently proposed decentralized colouring algorithm performs correctly in the multi-graph setting. We also present a new, extended version of this algorithm suited to a wide range of multi-radio architectures.