Flooding Time of Edge-Markovian Evolving Graphs

The authors introduce stochastic time-dependency in evolving graphs: starting from an initial graph, at every time step, every edge changes its state according to a two-state Markovian process with probabilities p and q. If an edge exists at time t, then, at time t + 1, it dies with probability q. If instead the edge does not exist at time t, then it will come into existence at time t + 1 with probability p. Such an evolving graph model is a wide generalization of time-independent dynamic random graphs and will be called edge-Markovian evolving graphs. The authors investigate the speed of information spreading in such evolving graphs. They provide nearly tight bounds on the completion time of the flooding mechanism aiming to broadcast a piece of information from a source node to all nodes. An interesting consequence of their results is that information spreading can be fast even if the graph, at every time step, is very sparse and disconnected.