The Effects of Locality on Efficient Distributed Computation

我们生活在一个互联互通日益紧密的时代。在一台机器上进行计算的时代即将结束，现在我们的系统通常由一组独立的设备组成，这些设备必须相互作用才能在没有中央协调器的情况下完成目标。这种转变带来了许多新的挑战，并迫使我们以不同的方式思考算法和计算。分布式算法设计的一个独特的中心问题是“局部性”，这个术语意味着每个设备可能拥有关于整个系统的非常有限的信息，或者只能查看附近的其他设备并与之通信。

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.