This paper considers several closely-related problems in synchronous dynamic networks with oblivious adversaries , and proves novel $$\varOmega (d + \text{ poly }(m))$$ 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 $$\varOmega (d)$$ Ω ( d ) lower bounds. Our novel lower bounds are hence the first non-trivial lower bounds and also the first lower bounds with a $$\text{ poly }(m)$$ poly ( m ) term. Our proof relies on a novel reduction from a certain two-party communication complexity problem. Our central proof technique is unique in the sense that we consider that communication complexity problem with a special leaker . The leaker helps Alice and Bob in the two-party problem, by disclosing to Alice and Bob certain “non-critical” information about the problem instance that they are solving.

中文翻译：

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动态网络中的一些下界与不经意的对手

这篇论文考虑了同步动态网络中几个密切相关的问题，并证明了它们的新 $$\varOmega (d + \text{ poly }(m))$$ Ω ( d + poly ( m ) ) 下界时间复杂度（以轮为单位）。这里d是动态网络的动态直径，m是节点总数。在这项工作之前，在无知的对手下，这些问题的唯一已知下界是微不足道的 $$\varOmega (d)$$Ω (d) 下界。因此，我们的新下界是第一个非平凡的下界，也是第一个具有 $$\text{ poly }(m)$$ poly ( m ) 项的下界。我们的证明依赖于某种两方通信复杂性问题的新颖减少。我们的中心证明技术是独一无二的，因为我们考虑了特殊泄密者的通信复杂性问题。