One of the big challenges in decentralized Wi-Fi networks is how to select channels for the different access points (APs) and their associated stations (STAs) in order to minimize interference and hence maximize throughput. Interestingly enough, de facto standards in terms of uncoordinated channel selection are quite simple, and in many cases result in fairly suboptimal channel allocations. Here, we explore how graph coloring can be used to evaluate and inform decisions on Wi-Fi channel selection in uncoordinated settings. Graph coloring, in its most basic form, is a classic mathematical problem where colors have to be assigned to nodes in a graph while avoiding assigning the same color to adjacent nodes. In this paper, we modeled Wi-Fi uncoordinated channel selection as a graph coloring problem and evaluated the performance of different uncoordinated channel selection techniques in a set of representative scenarios of residential buildings. The results confirm some of the widely accepted consensus regarding uncoordinated channel selection but also provide some new insights. For instance, in some settings, it would be better to delegate the decision on which channel to use to transmit the STAs, rather than having the AP make the decision on its own, which is the usual way.
Keywords: IEEE 802.11; channel assignment; graph coloring.