Distributed Online Data Aggregation in Dynamic Graphs

We consider the problem of aggregating data in a dynamic graph, that is, aggregating the data that originates from all nodes in the graph to a specific node, the sink. In our model, nodes are endowed with unlimited memory and unlimited computational power. Yet, we assume that communications between nodes are carried out with pairwise interactions, where nodes can exchange control information before deciding whether they transmit their data or not, given that each node is allowed to transmit its data at most once. When a node receives a data from a neighbor, the node may aggregate it with its own data. We are interested in giving lower bounds for this problem, under two possible adversaries: the oblivious adversary, and the randomized adversary that chooses the pairwise interactions uniformly at random. For the online adaptive and the oblivious adversary, we give impossibility results when nodes have no knowledge about the graph and are not aware of the future. For the randomized adversary, we propose two optimal algorithms, (i) when nodes have no knowledge at all and (ii) when each node knows its future pairwise interactions with the sink.