Analysis of the Diversification protocol Sample Clauses

Analysis of the Diversification protocol. ‌ We first introduce some notation that will be used throughout the analysis of our protocol. For simplicity, we assume that the colours are enumerated from 1 to k with i=1 corresponding weights w1, . . . , wk , where wi ⩾ 1 for i ∈ [k] , and we set w = Σk wi . Recall that cu(t) denotes the colour of agent u after the t-th iterations, and bu(t) its corresponding shade indicator after the t-th iterations: 1 for dark shade and 0 for light shade. We denote by Xx(t) and ai(t) the number of agents having colour i at time t with dark shade (bit value 1) and light shade (bit value 0), respectively, i.e., for t > 0 , Ai(t) = |{u : cu(t) = i, bu(t) = 1}| , and ai(t) = |{u : cu(t) = i, bu(t) = 0}| .
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