ITR/SI: On Topologies, Power Laws, and Hierarchies

最近的工作指出了真实世界网络的度分布中幂律的存在。回想起来，这些发现虽然被广泛宣传，但也许并不令人惊讶;几十年来，人们已经知道了现实世界现象中各种大小概念的幂律。然而，这些发现引发了人们对互联网结构和宏观属性的广泛兴趣。这种兴趣是及时的;最近的工作也揭示了网络拓扑属性可能会影响协议性能 生成真实的拓扑是理解拓扑对原型性能影响的前提。我们最近在拓扑生成方面的工作激发了我们提出的研究，并受到结构生成器和基于连通性的生成器之间的二分法的驱动，结构生成器明确体现了拓扑构造中的层次概念，而基于连通性的生成器则试图生成具有幂律度分布的拓扑. 我们对这个更大的问题的初步研究揭示了几个有趣的结果：真实的网络是由基于连通性的生成器很好地建模的，并且这些生成器导致具有连续层次结构的图。继续从这项工作，我们提出的研究将在temptto增加我们的真实的网络的结构，以及它们对协议性能的影响的基本理解。从概念上讲，我们提出的研究有三个相互关联的部分：理解真实的网络中的拓扑结构，设计基于HighlyOptimized Tolerance的拓扑结构模型，以及更密切地研究拓扑结构对协议性能的影响。 网络的结构及其对协议的影响直到最近才受到关注，就更广泛的影响而言，这项工作有可能在拓扑建模领域取得根本性的进展。从更广泛的意义上讲，它可能会开发出一些方法，用于理解导致其他现实世界网络（如Web拓扑和社交网络）发展的物理过程。

Recent work has pointed out the existence of power-laws in the degree distribution of real-worldnetworks. In retrospect, these findings while widely publicized are perhaps not surprising; power-lawsfor various notions of size in real-world phenomena have been known for several decades.Nevertheless, these findings have sparked extensive interest in the structure and macroscopic propertiesof the Internet. Such interest is timely; recent work has also revealed that network topology propertiesmay impact protocol performance Generating realistic topologies is a prerequisite for understanding the impact of topology on pro-tocolperformance. Our recent work on topology generation motivates the proposed research and isdriven by the perceived dichotomy between structural generators those that explicity embody somenotion of hierarchy in constructing topologies and connectivity-based generators those that at-temptto generate topologies with power-law degree distributions. Our preliminary research on this larger question reveals several interesting results: that real net-worksare well-modeled by connectivity-based generators, and that these generators result in graphswith a continuum of levels of hierarchy. Continuing on from this work, our proposed research will at-temptto increase our fundamental understanding of the structure of real networks, and their impact onprotocol performance. Conceptually, our proposed research has three interrelated parts: understand-inghierarchy in real networks, devising structural models for topology construction based on HighlyOptimized Tolerance, and examining more closely the impact of topology on protocol performance. The structure of networks, and their impact on protocols, has received little attention until recently.In terms of broader impact, this work has the potential for making fundamental progress in the areasof topology modeling. In a larger sense, it may develop methods that can be used to understand thephysical processes that lead to the development of other real-world networks, such as the Web topologyand social networks.