Some lower bounds in dynamic networks with oblivious adversaries
نویسندگان
چکیده
منابع مشابه
Some Lower Bounds in Dynamic Networks with Oblivious Adversaries
This paper considers several closely-related problems in synchronous dynamic networks with oblivious adversaries, and proves novel Ω(d + poly(m)) lower bounds on their time complexity (in rounds). Here d is the dynamic diameter of the dynamic network and m is the total number of nodes. Before this work, the only known lower bounds on these problems under oblivious adversaries were the trivial Ω...
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An oblivious subspace embedding (OSE) for some ε, δ ∈ (0, 1/3) and d ≤ m ≤ n is a distribution D over Rm×n such that for any linear subspace W ⊂ Rn of dimension d, P Π∼D (∀x ∈W, (1− ε)‖x‖2 ≤ ‖Πx‖2 ≤ (1 + ε)‖x‖2) ≥ 1− δ. We prove that any OSE with δ < 1/3 must have m = Ω((d + log(1/δ))/ε2), which is optimal. Furthermore, if every Π in the support of D is sparse, having at most s non-zero entries...
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ژورنال
عنوان ژورنال: Distributed Computing
سال: 2019
ISSN: 0178-2770,1432-0452
DOI: 10.1007/s00446-019-00360-4