时变图的建模与分析
Modeling and Analysis of Time-Varying Graphs
摘要：
我们生活在一个越来越多地被网络-通信、社会、信息、生物等-所支配的世界中，许多这些网络的一个核心属性是它们是动态的，也就是说，它们随着时间的推移表现出结构上的变化。虽然动态网络的实践已经激增，但我们在对网络动态性的基本数学理解方面落后了。对时变图的现有研究范围从初步的算法研究（例如，Ferreira关于演化图的工作）来分析动态随机图中的特定性质，如洪泛时间。研究动态图的一个流行模型是通过增加时间快照排列的一系列图。在本文中，我们研究了随时间变化的图中的可达性的基本属性，并根据两个度量来表征延迟，即存储或提前延迟和直通延迟。而不是期望值分析，我们集中在两个流行的动态随机图模型的随机间歇路径的路由延迟的精确概率分布的特征。使用这种分析，我们描述了多个时间图模型之间的准确性损失（在概率设置中），从一个保留所有时间排序信息的计算时间图属性的目的，到一个将各种快照折叠成一个图（一个称为粉碎的操作），具有多个中间变量。我们还展示了其他一些传统的图论性质可以扩展到时域。最后，我们提出了算法，用于控制在各种动态随机图的单副本自适应路由方案的数据包的进度。
英文摘要：
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While the practice of dynamic networks has proliferated, we lag behind in the fundamental, mathematical understanding of network dynamism. Existing research on time-varying graphs ranges from preliminary algorithmic studies (e.g., Ferreira's work on evolving graphs) to analysis of specific properties such as flooding time in dynamic random graphs. A popular model for studying dynamic graphs is a sequence of graphs arranged by increasing snapshots of time. In this paper, we study the fundamental property of reachability in a time-varying graph over time and characterize the latency with respect to two metrics, namely store-or-advance latency and cut-through latency. Instead of expected value analysis, we concentrate on characterizing the exact probability distribution of routing latency along a randomly intermittent path in two popular dynamic random graph models. Using this analysis, we characterize the loss of accuracy (in a probabilistic setting) between multiple temporal graph models, ranging from one that preserves all the temporal ordering information for the purpose of computing temporal graph properties to one that collapses various snapshots into one graph (an operation called smashing), with multiple intermediate variants. We also show how some other traditional graph theoretic properties can be extended to the temporal domain. Finally, we propose algorithms for controlling the progress of a packet in single-copy adaptive routing schemes in various dynamic random graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
