Channel Assignment with Separation for Special Classes of Wireless Networks: Grids and Rings

Given an integer u > 1, Q vector (61, 62, . . . ,6,-i) of nonnegative integers, end en undirected graph G = (V, E), an L(h62,. . . ,6,-I)-coloring of G is Q function f from the vertex set V to Q set of nonnegative integers such that If(u) f (v)l 2 &, if d(u,v) = i, 1 < i < u 1, where d(u, v) is the distance (i.e. the minimum number of edges) between the vertices u and v. An optimal L(&, 62,. . . , 6,-I)-coloring for G is one using the smallest range X of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e. colors) assigned to interfering stations (i.e. vertices) at distance i must be at least 6i apart, while the same channel can be reused in vertices whose distance is at least u. In pcarticuler, in this paper, the L(&, 1, . . . , 1)-coloting problem is considered on bidimensional grids and rings.