Bounds of Channel Assignment Problem for Cellular Networks Modelled as Triangular Grids

Cellular networks are often modelled as different regular grids and the channel assignment problem for interference avoidance is formulated as a coloring problem of the grid graph, where channels assigned to interfering stations 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 cellular networks modelled as triangular grids for the case where the co-channel reuse distance σ is 4 and the minimum channel separation δ_i is σ-i. We give the lower and upper bounds of the problem. And to obtain the upper bound, we present a channel assignment algorithm, which is potentially optimal.