2010/04/28 by Saber Jafarizadeh, Abbas Jamalipour, Jafarizadeh, Saber +1
Computer Science · Mathematics · #Discrete Mathematics (cs.DM) #Distributed #Distributed Control Multi-Agent Systems #Energy Efficient Wireless Sensor Networks #FOS: Computer and information sciences #Information Theory (cs.IT) #Optimization and Search Problems #Parallel #and Cluster Computing (cs.DC) #cs.DC #cs.DM #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1004.5094
11 pages, 13 figures, 1 table
openalex publication_date 2010/04/28 · arxiv created 2011/06/03 · arxiv updated 2011/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper studies the fastest distributed consensus averaging problem on branches of an arbitrary connected sensor network. In the previous works full knowledge about the sensor network's connectivity topology was required for determining the optimal weights and convergence rate of distributed consensus averaging algorithm over the network. Here in this work for the first time, the optimal weights are determined analytically for the edges of certain types of branches, independent of the rest of network. The solution procedure consists of stratification of associated connectivity graph of the branches and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions. Several examples and numerical results are provided to confirm the optimality of the obtained weights.