Improved Distributed Algorithms for Coloring Interval Graphs with Application to Multicoloring Trees

We give a distributed (1+)-approximation algorithm for the minimum vertex coloring problem on interval graphs, which runs in the LOCAL model and operates in O(1 log∗ n) rounds. If nodes are aware of their interval representations, then the algorithm can be adapted to the CONGEST model using the same number of rounds. Prior to this work, only constant factor approximations using O(log∗ n) rounds were known [12]. Linial’s ring coloring lower bound implies that the dependency on log∗ n cannot be improved. We further prove that the dependency on 1 is also optimal. To obtain our CONGEST model algorithm, we develop a color rotation technique that may be of independent interest. We demonstrate that color rotations can also be applied to obtain a (1 + )-approximate multicoloring of directed trees in O(1 log∗ n) rounds.