TY - JOUR

T1 - Clique Gossiping

AU - Liu, Yang

AU - Li, Bo

AU - Anderson, Brian D.O.

AU - Shi, Guodong

N1 - Publisher Copyright:
© 1993-2012 IEEE.

PY - 2019/12

Y1 - 2019/12

N2 - This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as linear dynamical systems. Such protocols become clique-gossip averaging algorithms when node states are scalars under averaging rules. We generalize the classical notion of line graph to capture the essential node interaction structure induced by both the underlying network and the specific clique sequence. We prove a fundamental eigenvalue invariance principle for periodic clique-gossip protocols, which implies that any permutation of the clique sequence leads to the same spectrum for the overall state transition when the generalized line graph contains no cycle. We also prove that for a network with n nodes, cliques with smaller sizes determined by factors of n can always be constructed leading to finite-time convergent clique-gossip averaging algorithms, provided n is not a prime number. Particularly, such finite-time convergence can be achieved with cliques of equal size m if and only if n is divisible by m and they have exactly the same prime factors. A proven fastest finite-time convergent clique-gossip algorithm is constructed for clique-gossiping using size- m cliques. Additionally, the acceleration effects of clique-gossiping are illustrated via numerical examples.

AB - This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as linear dynamical systems. Such protocols become clique-gossip averaging algorithms when node states are scalars under averaging rules. We generalize the classical notion of line graph to capture the essential node interaction structure induced by both the underlying network and the specific clique sequence. We prove a fundamental eigenvalue invariance principle for periodic clique-gossip protocols, which implies that any permutation of the clique sequence leads to the same spectrum for the overall state transition when the generalized line graph contains no cycle. We also prove that for a network with n nodes, cliques with smaller sizes determined by factors of n can always be constructed leading to finite-time convergent clique-gossip averaging algorithms, provided n is not a prime number. Particularly, such finite-time convergence can be achieved with cliques of equal size m if and only if n is divisible by m and they have exactly the same prime factors. A proven fastest finite-time convergent clique-gossip algorithm is constructed for clique-gossiping using size- m cliques. Additionally, the acceleration effects of clique-gossiping are illustrated via numerical examples.

KW - Gossip protocols

KW - averaging algorithms

KW - cliques

KW - scheduling

UR - http://www.scopus.com/inward/record.url?scp=85077338784&partnerID=8YFLogxK

U2 - 10.1109/TNET.2019.2952082

DO - 10.1109/TNET.2019.2952082

M3 - Article

SN - 1063-6692

VL - 27

SP - 2418

EP - 2431

JO - IEEE/ACM Transactions on Networking

JF - IEEE/ACM Transactions on Networking

IS - 6

M1 - 8906173

ER -