Pseudo-Random Graphs for Fast Consensus Protocol

In this paper, we focus on the design of network topology to achieve fast information distribution. We present the information distribution performance of Borel Cayley graphs, a family of pseudo-random graphs, is far superior than that of other well-known graph families. To demonstrate the effectiveness of this pseudo-random approach, we compare the convergence speed of the average consensus protocol on Borel Cayley graphs against that of a wide range of graph families with the sizes ranging from around 100 nodes to 5,000 nodes. In the comparison study, we compare the convergence speed of Borel Cayley graphs, regular ring lattices, Erdös-Rényi random graphs, Watts-Strogatz smallworld networks, and toroidal and diagonal meshes. Our results indicate that the proposed pseudo-random approach based on Borel Cayley graphs yields a 2 to 100 times faster convergence than the small-world network (rewiring probability p = 0.01, 0.1 and 0.2) does. More importantly, Borel Cayley graph has the best scalability over different graph sizes and degrees.