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Real-world Networks and Random Graph Models

现实世界的网络和随机图模型

基本信息

批准号：
226031825
负责人：
Professor Dr. Konstantinos Panagiotou
金额：
--
依托单位：
Mathematisches Institut
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/226031825?language=en
关键词：
Real world Networks Random Graph

项目摘要

Modeling the topology of large networks is a fundamental problem that has attracted considerable attention in the last decades. Networks provide an abstract way of describing relationships and interactions between elements of complex and heterogeneous systems. Examples include technological networks, like the World Wide Web or the Internet, biological networks, like the human brain, and social networks, which describe various kinds of interactions between individuals. An accurate mathematical model can have enormous impact on several research areas. From the viewpoint of computer science, an obvious benefit is that it could enable us to design more efficient algorithms that exploit the underlying topology. Moreover, the process of modeling may suggest and reveal novel types of qualitative network features, which become patterns to look for in datasets. Finally, an appropriate model will allow us to generate artificial instances, which resemble realistic instances to a high degree, for simulation purposes. Unfortunately, from today’s point of view, a significant proportion of the current literature is devoted only to experimental studies of properties of real-world networks, and there has been only little rigorous mathematical work. The aim of this project is twofold. First, by studying the typical structural properties of random networks generated by two carefully selected models, I want to investigate rigorously the fundamental underlying mechanisms that determine the formation of real-world networks. As a second step, I want to use the acquired knowledge to develop algorithms for many important optimization problems, like routing and information dissemination

大型网络的拓扑建模是过去几十年来引起广泛关注的一个基本问题。网络提供了一种描述复杂异构系统元素之间的关系和交互的抽象方法。例子包括技术网络，如万维网或互联网，生物网络，如人脑，以及社交网络，它们描述了个体之间的各种交互。准确的数学模型可以对多个研究领域产生巨大影响。从计算机科学的角度来看，一个明显的好处是它可以使我们能够设计更有效的算法来利用底层拓扑。此外，建模过程可能会建议并揭示新颖的定性网络特征类型，这些特征将成为在数据集中寻找的模式。最后，适当的模型将允许我们生成高度类似于现实实例的人工实例，以用于模拟目的。不幸的是，从今天的角度来看，当前文献的很大一部分仅致力于现实世界网络特性的实验研究，而严格的数学工作却很少。该项目的目标是双重的。首先，通过研究由两个精心选择的模型生成的随机网络的典型结构特性，我想严格研究决定现实世界网络形成的基本机制。第二步，我想利用所获得的知识来开发许多重要优化问题的算法，例如路由和信息传播