Topology Control for Computer Networks

随着信息和通信技术的进步，世界变得越来越紧密相连。通过更好地理解网络拓扑和相互作用的结构和动态，可以捕获、解释和改进许多自然现象和人造系统。本研究计划在早期计算几何和几何概率研究的基础上，重点研究计算机网络的拓扑控制，并进一步研究无线通信网络和云计算网络的随机几何和地理视角。例如，在无线通信网络中，接收到的信号和干扰强度取决于收发器和干扰器之间的距离，以及由于障碍物和多条传播路径而产生的阴影和衰落。使用云计算和分布式存储，用户请求和相关数据可以重定向到不同的位置并存储在不同的位置，这也会影响服务质量、系统效率以及抵御自然灾害和人为攻击的能力。因此，位置和距离在计算机网络中发挥着越来越重要的作用，特别是在拓扑控制方面，它影响着所有上层协议和功能。从图论的角度出发，我们在计算几何和几何概率方面的研究取得了一些突破，包括与菱形、六边形、规则三角形和不规则三角形相关的随机距离分布，以及最终有或没有参考点的任意多边形，具有广泛的应用。在提出的研究计划中，我们将继续研究物理和逻辑空间中的高阶，联合和条件距离分布，例如不同移动模型和路由方案的跳距离分布。通过考虑地理角度，我们提出的研究还将用户请求、计算和存储容量以及能源供应的时空动态纳入拓扑控制过程。拟议的研究还将继续培养具有高影响力研究贡献和高竞争就业机会的高素质人才，以造福加拿大和世界各地的经济和社会。

The world is connected and becomes increasingly so with the advances of information and communication technologies. Many natural phenomena and man-made systems can be captured, explained and improved by a better understanding of the structure and dynamics of the network topology and interactions. The proposed research program focuses on the topology control for computer networks, based on our early work on computational geometry and geometrical probability, and furthering into stochastic geometry with geographical perspectives, for both wireless communication networks and cloud computing networks. For example, in wireless communication networks, the received signal and interference strengths depend on the distances among transceivers and interferer, as well as shadowing and fading due to obstacles and multiple propagation paths. With cloud computing and distributed storage, user requests and associated data can be redirected to and stored at different locations, which also affect the service quality, system efficiency and the resilience against natural disasters and man-made attacks. Thus locations and distances play an increasingly important role in computer networks, particularly for topology control, based on which affect all upper-layer protocols and functions. Starting from a graph-theoretic perspective, our research in computational geometry and geometrical probability led to a few breakthroughs including the random distance distributions associated with rhombuses, hexagons, regular and irregular triangles, and eventually arbitrary polygons with or without a reference point, with a wide variety of applications. In the proposed research program, we will continue with high-order, joint and conditional distance distributions in both physical and logical spaces, e.g., hop distance distributions with different mobility models and routing schemes. By taking geographical perspectives into account, our proposed research will also incorporate the spatiotemporal dynamics of user requests, computation and storage capacities, and energy supplies into the topology control process. The proposed research will also continue the training of highly-qualified personnel with high-impact research contributions and high-competition job placement to benefit the economy and society in Canada and around the world.