Distributed coloring and communication in rings with local knowledge

We consider two interrelated tasks in a synchronous n-node ring: distributed constant coloring and local communication. Every node knows the labels of nodes up to a distance r from it, called the knowledge radius. In distributed constant coloring every node has to assign itself one out of a constant number of colors, so that adjacent nodes get different colors. In local communication every node has to communicate a message to both of its neighbors. We study these problems in two popular communication models: the one-way model in which each node can only either transmit to one neighbor or receive from one neighbor, in any round, and the radio model in which simultaneous receiving from two neighbors results in interference noise. We show that distributed constant coloring and local communication are tightly related and one can be used to accomplish the other. Also in most situations the optimal time is the same for both of them, and it strongly depends on knowledge radius