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Boolean Gossip Networks
Li, Bo1; Wu, Junfeng2; Qi, Hongsheng3,4; Proutiere, Alexandre5; Shi, Guodong6
AbstractThis paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions established regarding when the Boolean gossip process defines absorbing Markov chains. Particularly, it is shown that for the majority of the Boolean interaction rules, except for nine out of the total 2(16) - 1 possible nonempty sets of binary Boolean functions, whether the induced chain is absorbing has nothing to do with the topology of the underlying interaction graph, as long as connectivity is assumed. These results illustrate the possibilities of relating dynamical properties of Boolean networks to graphical properties of the underlying interactions.
KeywordBoolean networks gossiping process Markov chains communication classes
Funding ProjectNational Natural Science Foundation of China[11301518] ; National Natural Science Foundation of China[61333001] ; National Natural Science Foundation of China[61733018] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences ; Australian Department of Education and Training through an Endeavour Fellowship
WOS Research AreaComputer Science ; Engineering ; Telecommunications
WOS SubjectComputer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic ; Telecommunications
WOS IDWOS:000425324000009
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Document Type期刊论文
Corresponding AuthorWu, Junfeng
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
2.Zhejiang Univ, Coll Control Sci & Engn, Hangzhou 310027, Zhejiang, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
5.KTH Royal Inst Technol, Signals & Syst Linnaeus Ctr, Auton Complex Commun nEtworks, S-10044 Stockholm, Sweden
6.Australian Natl Univ, Res Sch Engn, Canberra, ACT 0200, Australia
Recommended Citation
GB/T 7714
Li, Bo,Wu, Junfeng,Qi, Hongsheng,et al. Boolean Gossip Networks[J]. IEEE-ACM TRANSACTIONS ON NETWORKING,2018,26(1):118-130.
APA Li, Bo,Wu, Junfeng,Qi, Hongsheng,Proutiere, Alexandre,&Shi, Guodong.(2018).Boolean Gossip Networks.IEEE-ACM TRANSACTIONS ON NETWORKING,26(1),118-130.
MLA Li, Bo,et al."Boolean Gossip Networks".IEEE-ACM TRANSACTIONS ON NETWORKING 26.1(2018):118-130.
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