AF: Small: Distributed Algorithmic Foundations of Dynamic Networks

该项目的总体目标是显著提高动态网络的分布式计算算法基础的最新水平。在动态网络中，网络的拓扑-节点(代表处理器/终端主机)和通信链路-随着时间的推移不断变化。现代网络技术，如对等网络、覆盖网络、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，并且容易受到攻击。分布式/分散式算法对于大规模通信网络的高效运行至关重要，例如，分布式最短路径算法用于因特网中的路由。直到最近，在过去三十年中发展起来的许多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开发坚实的理论基础。这样的基础对于充分发挥这些大规模网络的潜力至关重要，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。该项目将为在高度动态的网络中进行分布式计算奠定坚实的理论基础。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超大规模网络，对动态变化和大规模故障具有高度的健壮性，并且对网络中的恶意参与者是安全的。该项目将产生一个算法工具包，除了为实践者提供算法性能保证和理论基准外，还将为在动态网络中执行分布式计算提供构建块。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，即能够以分散方式测量、监控和调节自身的网络。PI计划开发一门关于分布式网络算法的新课程和一本与所进行的研究密切相关的教科书。这项研究将积极涉及博士后研究人员、研究生和本科生。该项目有两个关键的研究目标。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构件，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环境中研究上述问题，其中还可能包括拜占庭(恶意)节点的存在，这些节点可能试图破坏分布式算法。该项目还将研究分布式算法的性能下限，包括可以容忍的动态量。其次，它将开发全分布式算法，用于计算网络的关键全局指标，并维护具有所需特性的动态网络。这解决了一个重要的问题，该问题对第一个目标是补充的，也是关键的，即如何测量动态网络的基本参数，例如其大小、连通性、电导、平均度和其他与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的拓扑属性的动态网络，如小直径、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，即使在高动态和大量拜占庭节点存在的情况下，该算法也具有健壮性和容错性。该项目将建立在PI和他的合作者最近开发的动态网络分布式算法框架的基础上，并显著扩展该框架。

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.