The Effects of Locality on Efficient Distributed Computation

我们生活在一个日益互联的时代。在一台机器上进行计算的日子即将结束，现在我们的系统通常由一组独立的设备组成，这些设备必须在没有中央协调器的情况下进行交互以实现目标。这种转变带来了许多新的挑战，迫使我们以不同的方式思考算法和计算。分布式算法设计所独有的一个核心问题是“局部性”，这一术语意味着每个设备可能具有关于整个系统的非常有限的信息，或者只能查看和与附近的其他设备通信。 我们在这项研究中的目标是更好地理解不同程度的局部性如何影响分布式算法的效率。我们从广义上考虑效率的概念，因为不同的应用程序在资源消耗方面有不同的优先级。效率的三个重要指标是：时间（算法有多快）、成本（运行算法需要多少钱或燃料）和通信（网络带宽要求）。我们的主要贡献将是正式和精确地分析算法的效率（相对于上面列出的三个措施）和局部约束之间的权衡。更具体地说，这涉及到产生两种结果： (1)描述当信息和/或设备能力受限时的有效算法，以及， (2)证明不可能的结果，给出最好的效率界限，我们可以希望在这样的限制。 我们已经确定了四个应用领域，我们将在这些领域集中努力，以取得这些成果： (Area 1）具有同步通信的静态网络 (Area 2）具有无线电通信的移动的节点的网络 (Area 3.未知环境中的自主机器人 (Area 4）在具有有界缓冲区的网络中路由分组 在未来5年，我计划在上述每个应用领域完成以下项目： (Area 1）在所有可能的信息局部性范围内确定最优的领袖选举算法。 (Area 2）在信息限制和通信/感测限制下，确定用于在简单道路网络上行驶的车辆的最佳邻居发现算法。 (Area 3）在通信和视觉受限的未知环境中确定自主机器人的最优会合算法。 (Area 4）确定用于在网络中转发分组的最佳策略，其中每个路由器具有小的存储器缓冲区和关于网络的其余部分的有限信息。 我计划在未来5年内直接培训8-10名HQP，我将在我们新成立的合作研究实验室间接参与其他HQP的培训。

We live in an era of increasing connectivity. The days where computation happens at a single machine are coming to an end, and now our systems often comprise of a set of independent devices that have to interact to accomplish a goal without a central coordinator. This shift has introduced many new challenges and has forced us to think about algorithms and computation in a different way. One central issue that is unique to distributed algorithm design is that of "locality", a term that means that each device might have very limited information about the entire system, or can only view and communicate with other nearby devices. Our goal in this research is to better understand how different degrees of locality affect how efficient distributed algorithms can be. We consider the notion of efficiency in a broad sense, since different applications have different priorities with respect to resource consumption. Three important measures of efficiency are: time (how fast is the algorithm), cost (how much money or fuel does it take to run the algorithm), and communication (what are the network bandwidth requirements). Our main contributions will be to formally and precisely analyze the tradeoff between the efficiency of algorithms (with respect to the three measures listed above) and locality constraints. More specifically, this involves producing two kinds of results: (1) describing efficient algorithms when information and/or device capabilities are restricted, and, (2) proving impossibility results that give the best efficiency bounds that we can hope for under such restrictions. We have identified four application areas where we will focus our efforts in producing these kinds of results: (Area 1) Static Networks with Synchronous Communication (Area 2) Networks of Mobile Nodes with Wireless Radio Communication (Area 3) Autonomous Robots in Unknown Environments (Area 4) Routing Packets in Networks with Bounded Buffers In the next 5 years, I plan to complete the following projects within each of the above application areas: (Area 1) Determining the optimal leader election algorithms under all possible ranges of information locality. (Area 2) Determining the optimal neighbour discovery algorithms for vehicles traveling on simple road networks, both under information restrictions and communication/sensing restrictions. (Area 3) Determining the optimal rendezvous algorithms for autonomous robots in an unknown environment with limited communication and vision. (Area 4) Determining the best strategy for forwarding packets in a network where each router has a small memory buffer and limited information about the rest of the network. I plan to directly train 8-10 HQP in the next 5 years, and I will be indirectly involved in the training of other HQP in our newly-formed collaborative research lab.