Percolation theory aided data diffusion for mobile wireless networks

In this paper, we investigate the data diffusion for mobile wireless networks using percolation theoretic approaches. By considering the impacts of both node mobility and the willingness of node for the message on the data diffusion probability, we employ a one-dependent percolation model to characterize and analyze the diffusion of data on a general directed and locally finite graph. To model the node heterogeneities in networks, we assign a two-dimensional random weight vector to each vertex of the graph. The probability of an edge being open depends on the weights of its end vertices. Conditionally on the weights, the states of the edges are independent of each other. In a mobile wireless network scenario, the vertex of the graph represents the network node, and the edge denotes the network communication link. The two components of the weight vector assigned to the network node denote its meeting probability with other nodes and the willingness probability of it for the message, respectively. By controlling the corresponding quantities for independent bond percolation with a certain density, we can bound the percolation probability from a given node to another one as well as the expected number of nodes that can be reached by an open path starting at a given node.