Properties and definition of the protocol Sample Clauses

Properties and definition of the protocol. ‌ We now introduce the properties we will study in this Diversification protocol: di- versity, fairness, and sustainability. The primary goal is to achieve diversity, and the two secondary goals are fairness and sustainability. We assume that both the total weight w and the number of colours k are independent of the size of the population, and both are constant. (i) Diversity. A protocol is diverse if there exists t0 ⩾ 0 and T = Ω(nα) , where α > 0 is a constant, such that for any t ∈ {t0, . . . , T } and i ∈ [k] w.h.p.3 Ci(t) wi ˜ 1 − n w = O √n (3.1) Note that, ‘O˜ (f (n))’ is the soft O notation, meaning ‘O (f (n) · polylog(f (n)))’ ,
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