AbstractGiven a vector (δ1,δ2,…,δt) of nonincreasing positive integers, and an undirected graph G = (V,E), an L(δ1,δ2,…,δt)‐coloring of G is a function f from the vertex set V to a set of nonnegative integers such that ∣f(u) − f(v)∣ ≥ δi, 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. An optimal L(δ1,δ2,…,δt)‐coloring for G is one minimizing the largest integer used over all such colorings. Such a coloring problem has relevant applications in channel assignment for interference avoidance in wireless networks. This article presents efficient approximation algorithms for L(δ1,δ2,…,δt)‐coloring of two relevant classes of graphs—trees, and interval graphs. Specifically, based on the notion of strongly simplicial vertices, O(n(t + δ1)) and O(nt2δ1) time algorithms are proposed to find α‐approximate colorings on interval graphs and trees, respectively, where n is the number of vertices and α is a constant depending on t and δ1,…,δt. Moreover, an O(n) time algorithm is given for the L(δ1,δ2)‐coloring of unit interval graphs, which provides a 3‐approximation. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 49(3), 204–216 2007