Clique Gossiping
Liu, Yang1; Li, Bo2; Anderson, Brian D. O.1,3; Shi, Guodong1,4
AbstractThis 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.
KeywordGossip protocols cliques scheduling averaging algorithms
Indexed BySCI
Funding ProjectAustralian Research Council (ARC)[DP190103615] ; National Natural Science Foundation of China (NSFC)[61873262]
WOS Research AreaComputer Science ; Engineering ; Telecommunications
WOS SubjectComputer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic ; Telecommunications
WOS IDWOS:000505578800018
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Document Type期刊论文
Corresponding AuthorShi, Guodong
Affiliation1.Australian Natl Univ, Res Sch Elect Energy & Mat Engn, Canberra, ACT 0200, Australia
2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
3.Hangzhou Dianzi Univ, Hangzhou 310018, Zhejiang, Peoples R China
4.Univ Sydney, Australian Ctr Field Robot, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW 2006, Australia
Recommended Citation
GB/T 7714
Liu, Yang,Li, Bo,Anderson, Brian D. O.,et al. Clique Gossiping[J]. IEEE-ACM TRANSACTIONS ON NETWORKING,2019,27(6):2418-2431.
APA Liu, Yang,Li, Bo,Anderson, Brian D. O.,&Shi, Guodong.(2019).Clique Gossiping.IEEE-ACM TRANSACTIONS ON NETWORKING,27(6),2418-2431.
MLA Liu, Yang,et al."Clique Gossiping".IEEE-ACM TRANSACTIONS ON NETWORKING 27.6(2019):2418-2431.
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