Analysis of Brownian Particles for finding the shortest path in networks

Abstract

In this paper, we propose a method to analyze the shortest path finding between two nodes in complex networks. In this method, we first find that single Brownian particle follows the shortest path between source node and destination node in the probability of where denotes the shortest path steps between two nodes. To be compared with single particle utilization, then we specially analyze the multiple particles. We compute the probability of particles’ taking the shortest path between and when particles starts simultaneously from the source and head to the destination as . It’s very clear that there must be particles taking the shortest path to arrive at the destination in the multiple particles environment. And with the number of increasing, the arriving probability first arise and then drop down rapidly until to zero. In the end, we make the experiments and confirm our theoretical analysis. Our results would provide valuable usage for some applications such as finding the optimal routing in wireless sensor networks.

DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3071