Channel assignment on strongly-simplicial graphs

Abstract

Given a vector (/spl delta//sub 1/, /spl delta/2,..., /spl delta//sub t/) of non increasing positive integers, and an undirected graph G = (V, E), an L(/spl delta//sub 1/, /spl delta/2,..., /spl delta//sub 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)| /spl ges/ /spl delta//sub i/, if d(u, v) = i, 1 /spl les/ i /spl les/ 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(/spl delta//sub 1/, 1,..., 1)-colorings of trees and interval graphs, as well as approximate L(/spl delta//sub 1/, /spl delta//sub 2/) colorings of unit interval graphs.