Distributed Algorithms for Coloring Interval Graphs

We explore the question how well we can color graphs in distributed models, especially in graph classes for which ∆+ 1-colorings provide no approximation guarantees. We particularly focus on interval graphs. In the LOCAL model, we give an algorithm that computes a constant factor approximation to the coloring problem on interval graphs in O(log∗ n) rounds, which is best possible. The result holds also for the CONGEST model when the representation of the nodes as intervals is given. We then consider restricted beep models, where communication is restricted to the aggregate acknowledgment of whether a node’s attempted coloring succeeds. We apply an algorithm designed for the SINR model and give a simplified proof of a O(logn)-approximation. We show a nearly matching Ω(logn/ log logn)-approximation lower bound in that model.