Mixing search on complex networks

In this article, we derive the first passage time (FPT) distribution and the mean first passage time (MFPT) of random walks from multiple sources on networks. On the basis of analysis and simulation, we find that the MFPT drops substantially when particle number increases at the first stage, and converges to the shortest distance between the sources and the destination when particle number tends to infinite. Given the fact that a Brownian particle from a high-degree node often needs a large number of steps to reach an expected low-degree node, which is the bottleneck for a single random walk, we propose a mixing search model to improve the efficiency of search processes by using random walks from multiple sources to continue the searches from high-degree nodes to destinations. We compare our model with the mixing navigation model proposed by Zhou on complex networks and find that our model converges much faster with lower hardware cost than Zhou’s model. Moreover, simulations on scale-free networks show that the search efficiency of our model is much higher than that of a single random walk, and comparable to that of multiple random walks which have much higher hardware cost than our model. Finally, we discuss the traffic cost of our model, and propose an absorption strategy for our model to recover the additional walkers in networks. Simulations indicate that this strategy reduces the traffic cost of our model effectively.