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Optimal strategies in the average consensus problem (0708.3220v1)
Published 23 Aug 2007 in cs.MA, cs.NI, and math.OC
Abstract: We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.