The Cost of Unknown Diameter in Dynamic Networks

Haifeng Yu, Yuda Zhao, Irvan Jahja
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引用次数: 4

Abstract

For dynamic networks with unknown diameter, we prove novel lower bounds on the time complexity of a range of basic distributed computing problems. Together with trivial upper bounds under dynamic networks with known diameter for these problems, our lower bounds show that the complexities of all these problems are sensitive to whether the diameter is known to the protocol beforehand: Not knowing the diameter increases the time complexities by a large poly(N) factor as compared to when the diameter is known, resulting in an exponential gap. Our lower bounds are obtained via communication complexity arguments and by reducing from the two-party DisjointnessCP problem. We further prove that sometimes this large poly(N) cost can be completely avoided if the protocol is given a good estimate on N. In other words, having such an estimate makes some problems no longer sensitive to unknown diameter.
动态网络中未知直径的代价
对于直径未知的动态网络,我们证明了一系列基本分布式计算问题的时间复杂度的下界。与这些问题在已知直径的动态网络下的微不足道的上界一起,我们的下界表明,所有这些问题的复杂性对协议是否事先已知直径很敏感:与直径已知时相比,不知道直径会使时间复杂性增加一个大的poly(N)因子,从而导致指数差距。我们的下界是通过对通信复杂度的论证和对两方不连接问题的约简得到的。我们进一步证明,如果协议给出一个很好的N估计,有时可以完全避免这种大的poly(N)代价。换句话说,有了这样的估计,一些问题对未知直径不再敏感。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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