Information spreading in stationary markovian evolving graphs

Markovian evolving graphs [2] are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network scenarios. We study the speed of information spreading in the stationaryphase by analyzing the completion time of the flooding mechanism. We prove a general theorem that establishes an upper bound on flooding time in any stationary Markovian evolving graph in terms of its node-expansion properties. We apply our theorem in two natural and relevant cases of such dynamic graphs: edge-Markovian evolving graphs [24, 7] where the probability of existence of any edge at time t depends on the existence (or not) of the same edge at time t-1; geometric Markovian evolving graphs [4, 10, 9] where the Markovian behaviour is yielded by n mobile radio stations, with fixed transmission radius, that perform n independent random walks over a square region of the plane. In both cases, the obtained upper bounds are shown to be nearly tight and, in fact, they turn out to betight for a large range of the values of the input parameters. © 2009 IEEE.