Broadcasting with universal lists

In broadcasting, information originally held in one node of a communication network (called the source) has to be transmitted to all other nodes. In a unit of time, every node which already received the source message can transmit it to one neighbor. In classical broadcasting, the choice of neighbors to be informed by a node and the order in which they are informed may depend on the source. Thus, nodes need to store many transmission lists corresponding to different possible sources and need to know the source to adapt their behavior accordingly. In this paper, we consider a variant of broadcasting in which every node is given a priori a single ordered list containing some of its neighbors. This list is meant to be universal for all possible sources. Upon obtaining the source message, a node transmits it to the neighbors from its list in prescribed order and then stops. This requires substantially less local memory devoted to schedule communication but usually increases broadcasting time. We compare broadcasting time in this and in the classical model and design optimal broadcasting schemes in the universal-list model for trees, rings, and grids. For tori and for complete graphs, we give upper bounds on broadcasting time.