节点间时延受限的海缆网络最优树形拓扑
Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency
摘要：
针对三维欧氏空间中不规则二维流形上的树型拓扑网络，提出了一种优化的电缆路径规划方法，并将其应用于海缆网络的规划。我们的解决方案是基于总成本最小化，其中的个别电缆成本被假定为线性的相应的海缆的长度受到延迟的限制对节点之间。这些延迟约束限制了任何节点对之间的电缆长度和跳数。我们的方法结合了快速推进法（FMM）和一个新的最小生成树（MST）的最小线性规划（ILP）制定有约束的节点对之间。我们注意到这个带约束的MST问题是NP-完全的。然而，我们证明了ILP的运行时间是足够的绝大多数现有的电缆系统。对于ILP无法在可接受的时间内找到最优解的电缆系统，我们提出了一种基于Prim算法的替代启发式算法。此外，我们应用我们的FMM/ILP为基础的算法，以现实世界中的电缆路径规划的例子，并证明它可以有效地找到一个MST与节点对之间的延迟约束。
英文摘要：
This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on total cost minimization, where the individual cable costs are assumed to be linear to the length of the corresponding submarine cables subject to latency constraints between pairs of nodes. These latency constraints limit the cable length and number of hops between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Tree (MST) where there are constraints between pairs of nodes. We note that this problem of MST with constraints is NP-complete. Nevertheless, we demonstrate that ILP running time is adequate for the great majority of existing cable systems. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose an alternative heuristic algorithm based on Prim's algorithm. In addition, we apply our FMM/ILP-based algorithm to a real-world cable path planning example and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes.
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