In a model of network communication based on a random walk in an undirected graph, what subset of nodes (subject to constraints on its size), enable the fastest spread of information? The dynamics of spread is described by a process dual to the movement from informed to uninformed nodes. In this setting, an optimal set A minimizes the sum of the expected first hitting time F(A), of random walks that start at nodes outside the set. In this paper, the problem is reformulated so that the search for solutions to the problem is restricted to a class of optimal and near optimal subsets of the graph. We introduce a sub- modular, non-decreasing rank function,that permits some comparison between the solution obtained by the classical greedy algorithm and one obtained by our methods.
Journal of Research (NIST JRES) -
random walk, connected graph, network, first hitting time