Convergence time evaluation of a gossip algorithm over signed graphs

Nguyen Thi Hoai Linh, Takayuki Wada, Izumi Masubuchi, Toru Asai, Yasumasa Fujisaki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Convergence time is investigated for a gossip algorithm over a connected signed graph, where each edge of the graph has positive or negative sign. The algorithm is an iterative procedure. At each time, (i) two nodes directly connected with an edge are chosen randomly, (ii) they exchange their values according to the sign of the edge, and (iii) they update their values as the average of each node's value and its received value. It is shown that the values of the algorithm always converge in mean square, where a bipartite consensus or a trivial consensus is achieved. A convergence time is defined as the smallest time such that it takes for the values of the algorithm to get within a given neighborhood of the consensus value with high probability, regardless of initial state. An upper bound of the convergence time is given in terms of a characteristic value of the given graph.

Original languageEnglish
Title of host publication2015 10th Asian Control Conference
Subtitle of host publicationEmerging Control Techniques for a Sustainable World, ASCC 2015
EditorsHazlina Selamat, Hafiz Rashidi Haruna Ramli, Ahmad Athif Mohd Faudzi, Ribhan Zafira Abdul Rahman, Asnor Juraiza Ishak, Azura Che Soh, Siti Anom Ahmad
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479978625
DOIs
Publication statusPublished - Sep 8 2015
Externally publishedYes
Event10th Asian Control Conference, ASCC 2015 - Kota Kinabalu, Malaysia
Duration: May 31 2015Jun 3 2015

Publication series

Name2015 10th Asian Control Conference: Emerging Control Techniques for a Sustainable World, ASCC 2015

Other

Other10th Asian Control Conference, ASCC 2015
CountryMalaysia
CityKota Kinabalu
Period5/31/156/3/15

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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