AF: Small: Distributed Algorithmic Foundations of Dynamic Networks

该项目的总体目标是显著推进动态网络分布式计算算法基础的最新技术。在动态网络中，网络拓扑——节点（表示处理器/终端主机）和通信链路——会随着时间不断变化。现代网络技术，如点对点网络、覆盖网络和自组织无线和移动网络，本质上是非常动态的；此外，它们资源受限、不可靠且容易受到攻击。分布式/去中心化算法对于大规模通信网络的有效运行至关重要，例如，分布式最短路径算法用于Internet中的路由。直到最近，过去三十年中发展起来的分布式算法理论主要集中在静态网络上；因此，其结果不适用于动态网络。这就需要为动态网络的健壮、安全和可扩展的分布式计算提供坚实的理论基础。这样的基础是实现这些大规模网络的全部潜力的关键，这些网络具有广泛的应用，包括通信、数据存储和检索、环境监测、电子商务、资源分配和共享以及搜索。该项目将为高度动态网络中的分布式计算发展一个严谨的理论基础。特别是，它将开发和分析分布式算法，这些算法可以很好地扩展到非常大型的网络，对动态变化和大规模故障具有高度鲁棒性，并且可以安全地抵御网络中的恶意参与者。该项目将产生一个算法工具包，该工具包将为在动态网络中执行分布式计算提供构建块，并为从业者提供性能保证和理论基准的算法。该项目有可能影响拓扑感知和自我调节网络的设计和工程，即可以以分散的方式测量、监控和调节自己的网络。PI计划开发与所进行的研究密切相关的分布式网络算法的新课程和教科书。这项研究将积极参与博士后、研究生和本科生的研究。该项目有两个主要的研究目标。首先，它将设计和分析可扩展和健壮的分布式算法，用于基本的分布式计算问题，包括协议、领导者选举、存储和搜索以及路由。这些问题是分布式计算的基本组成部分，得到了广泛的应用。出于容错和安全考虑，该项目将在对抗性动态设置中研究上述问题，其中还可能包括可能试图挫败分布式算法的拜占庭（恶意）节点的存在。该项目还将研究分布式算法性能的下限，包括可以容忍的动态量。其次，它将开发用于计算网络关键全局指标的完全分布式算法，并保持具有理想属性的动态网络。这解决了一个重要的问题，这是互补的，也是关键的第一个目标，即如何测量一个动态网络的基本参数，如它的大小，连通性，电导，平均度和其他节点相关的统计数据。一个相关的目标是构建和维护具有良好拓扑特性的动态网络，如低直径、高连通性和高电导。在上述两个研究目标中，关键的挑战是设计可扩展的分布式算法，即使在大量动态和大量拜占庭节点存在的情况下也要具有鲁棒性和容错性。该项目将建立并显著扩展PI及其合作者最近开发的动态网络分布式算法框架。

The overarching goal of this project is to significantly advance the state of the art in the algorithmic foundations of distributed computing for dynamic networks. In a dynamic network, the topology of the network---both nodes (representing processors/endhosts) and communication links---changes continuously over time. Modern networking technologies such as peer-to-peer networks, overlay networks, and ad hoc wireless and mobile networks, are inherently very dynamic; furthermore, they are resource-constrained, unreliable, and vulnerable to attacks. Distributed/decentralized algorithms are critical to the efficient operation of large-scale communication networks, e.g., distributed shortest paths algorithms are used for routing in the Internet. Till recently, much of the distributed algorithmic theory developed over the last three decades has focused mainly on static networks; as such its results do not apply to dynamic networks. This necessitates the development of a solid theoretical foundation for robust, secure, and scalable distributed computing for dynamic networks. Such a foundation is critical to realize the full potential of these large-scale networks that have a wide variety of applications including communication, data storage and retrieval, environment monitoring, electronic commerce, resource distribution and sharing, and search.The project will develop a rigorous theoretical foundation for distributed computing in highly dynamic networks. In particular, it will develop and analyze distributed algorithms that scale well to very large-sized networks, are highly robust to dynamic changes and large-scale failures, and are secure against malicious participants in the network. The project will result in an algorithmic toolkit which will provide the building blocks for performing distributed computation in dynamic networks, besides providing algorithms with performance guarantees and theoretical benchmarks for practitioners. The project has the potential to impact the design and engineering of topologically-aware and self-regulating networks, i.e., networks that can measure, monitor, and regulate themselves in a decentralized fashion. The PI plans to develop a new course and a textbook on distributed network algorithms that is closely related to the research undertaken. This research will actively involve postdoctoral researchers, graduate students, and undergraduate students.The project has two key research goals. First, it will design and analyze scalable and robust distributed algorithms for fundamental distributed computing problems including agreement, leader election, storage and search, and routing. These problems are basic building blocks in distributed computing and are widely used. Motivated by fault-tolerance and security considerations, the project will study the above problems in an adversarial dynamic setting, that can also include the presence of Byzantine (malicious) nodes which may try to foil the distributed algorithm. The project will also study lower bounds on the performance of distributed algorithms including the amount of dynamism that can be tolerated. Second, it will develop fully-distributed algorithms for computing key global metrics of a network and to maintain dynamic networks with desirable properties. This addresses an important issue that is complementary and also critical to the first goal, i.e., how to measure basic parameters of a dynamic network such as its size, connectivity properties, conductance, average degree and other node-related statistics. A related goal is to construct and maintain dynamic networks with good topological properties such as low diameter, high connectivity, and high conductance. In both the above research goals, the key challenge is to design scalable distributed algorithms that are robust and fault-tolerant even under a high amount of dynamism and the presence of a large amount of Byzantine nodes. The project will build on and significantly extend the distributed algorithmic framework for dynamic networks that was recently developed by the PI and his collaborators.