One-Step Memory Random Walk on Complex Networks: An Efficient Local Navigation Strategy

Abstract

We propose one-step memory random walk on complex networks for which at each time step, the walker will not be allowed to revisit the last position. Mean first passage time is adopted to quantify its search efficiency and a procedure is provided for calculating it analytically. Interestingly, we find that in the same circumstance, one-step memory random walk usually takes less time than random walk for finding a target given in advance. Furthermore, this navigation strategy presents a better performance even in comparison with corresponding optimal biased random walk when moving on networks without small-world effect. Our findings are confirmed on two canonical network models and a number of real networks. Our work reveals that one-step memory random walk is an efficient local search strategy, which can be applied to transportation and information spreading.