Channel assignment on strongly-simplicial graphs

Given a vector (δ₁, δ2,..., δ_t) of non increasing positive integers, and an undirected graph G = (V, E), an L(δ₁, δ2,..., δ_t)-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that |f(u) - f (v)| ≥ δ_i, if d(u, v) = i, 1 ≤ i ≤ t, where d(u,v) is the distance (i.e. the minimum number of edges) between the vertices u and v. This paper presents efficient algorithms for finding optimal L(1,..., 1)-colorings of trees and interval graphs. Moreover, efficient algorithms are also provided for finding approximate L(δ₁, 1,..., 1)-colorings of trees and interval graphs, as well as approximate L(δ₁, δ₂) colorings of unit interval graphs.