Deterministic radio broadcasting

We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are not assumed to know their neighbors, nor the size of the network, they are aware only of their individual identifying numbers. If more than one message is delivered to a node in a step then the node cannot hear any of them. Nodes cannot distinguish between such collisions and the case when no messages have been delivered in a step. The fastest previously known deterministic algorithm for deterministic distributed broadcasting in unknown radio networks was presented in [6], it worked in time O(n^11/6). We develop three new deterministic distributed algorithms. Algorithm A develops further the ideas of [6] and operates in time O(n^1.77291) = O(n^9/5), for general networks, and in time O(n^{1+a+H(a)+o(1)}) for sparse networks with in-degrees O(n^a) for a < 1/2; here H is the entropy function. Algorithm B uses a new approach and works in time O(n^3/2 log^1/2 n) for general networks or O(n^1+a+o(1)) for sparse networks. Algorithm C further improves the performance for general networks running in time O(n^3/2).