Leader selection for fast consensus in networks

¹ Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China - Shanghai 200240, PRC
² Key Laboratory of Advanced Control and Optimization for Chemical Processes (East China University of Science and Technology), Ministry of Education - Shanghai 200237, PRC

^(a) xfwang@sjtu.edu.cn

Received: 6 August 2015
Accepted: 25 November 2015

Abstract

This paper considers a leader-follower system with the aim to select an optimal leader so as to drive the remaining nodes to reach the desired consensus with the fastest convergence speed. An index called consensus centrality (CC) is proposed to quantify how fast a leader could guide the network to achieve the desired consensus. The experiment results explored the big similarities between the distributions of CC and degree in the network, which suggest that the suboptimal leader selected by the maximum degree can approximately approach the optimal leader in heterogeneous networks. Combining the degree-based k-shell decomposition with consensus centrality, a leader selection algorithm is proposed to reduce the computational complexity in large-scale networks. Finally, the convergence time of an equivalent discrete-time model is given to illustrate the properties of the suboptimal solutions.