Optimal Channel Assignment for Wireless Networks Modelled as Hexagonal and Square Grids

Wireless networks are often modelled as different grids and the channel assignment problem for interference avoidance is formulated as a coloring problem of the grid graph, where channels (i.e., colors) assigned to interfering stations (i.e., vertices) at distance i must be at least δ_i apart, while the same channel can be reused in vertices whose distance is at least σ. In this paper, we consider the channel assignment problem for wireless networks modelled as hexagonal and square grids. We present optimal channel assignment algorithms for the case where the co-channel reuse distance σ is 4 and the minimum channel separation δ_i is σ-i.