@article{6f05067fb34048b8af963dec3b0d3be4,
title = "Gossip over holonomic graphs",
abstract = "A gossip process is an iterative process in a multi-agent system where only two neighboring agents communicate at each iteration and update their states. The neighboring condition is by convention described by an undirected graph. In this paper, we consider a general update rule whereby each agent takes an arbitrary weighted average of its and its neighbor's current states. In general, the limit of the gossip process (if it converges) depends on the order of iterations of the gossiping pairs. The main contribution of the paper is to provide a necessary and sufficient condition for convergence of the gossip process that is independent of the order of iterations. This result relies on the introduction of the novel notion of holonomy of local stochastic matrices for the communication graph. We also provide complete characterizations of the limit and the space of holonomic stochastic matrices over the graph.",
keywords = "Consensus, Convergence of matrix products, Gossiping, Holonomy, Markov processes",
author = "Xudong Chen and Belabbas, {Mohamed Ali} and Ji Liu",
note = "Funding Information: This work was supported by the National Science Foundation [ ECCS-1809076 , ECCS-1809315 ], the Air Force Office of Scientific Research [ FA9550-20-1-0076 , FA9550-20-1-0333 ], and the U.S. Army Research Laboratory [ W911NF-21-2-0098 ]. Funding Information: Xudong Chen is Assistant Professor in the Department of Electrical, Computer, and Energy Engineering at the University of Colorado Boulder. Prior to that, he was a postdoctoral fellow in the Coordinated Science Laboratory at the University of Illinois, Urbana-Champaign. He obtained the B.S. degree from Tsinghua University, China, in 2009, and the Ph.D. degree in Electrical Engineering from Harvard University, Massachusetts, in 2014. He is an awardee of the 2020 Air Force Young Investigator Program, a recipient of the 2021 NSF Career Award, and the recipient of the 2021 Donald P. Eckman Award. His current research interests are in the area of control theory, stochastic processes, optimization, game theory, and their applications in large-scale complex systems. Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",
year = "2022",
month = feb,
doi = "10.1016/j.automatica.2021.110088",
language = "English (US)",
volume = "136",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
}