在超短时间内导航超小世界
Navigating ultrasmall worlds in ultrashort time
摘要：
随机无标度网络是超小世界。在规模为N的网络中，最短路径的平均长度为lnlnN。在这里，我们展示了这些超小的世界可以在超短时间内导航。嵌入度量空间的无标度网络上的贪婪路由发现平均长度缩放也为lnlnN的路径。贪婪路由只使用本地信息来导航网络。然而，它发现渐近的最短路径，直接计算需要全局拓扑知识。我们的研究结果意味着，复杂网络的特殊结构，确保缺乏全局拓扑意识的通信路径的长度渐近没有影响。这些结果有重要的后果，如互联网，在保持当前的拓扑知识的通信系统是一个主要的可扩展性瓶颈。
英文摘要：
Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free networks embedded in metric spaces finds paths with the average length scaling also as lnlnN. Greedy routing uses only local information to navigate a network. Nevertheless, it finds asymptotically the shortest paths, a direct computation of which requires global topology knowledge. Our findings imply that the peculiar structure of complex networks ensures that the lack of global topological awareness has asymptotically no impact on the length of communication paths. These results have important consequences for communication systems such as the Internet, where maintaining knowledge of current topology is a major scalability bottleneck.
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