Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency

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 between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Trees (MST) where there are constraints between pairs of nodes. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose two polynomial-time heuristic methods based on Prim's algorithm, which we call PRIM I and PRIM II. PRIM I starts with an arbitrary initial node, while PRIM II iterates PRIM I over all nodes. A comprehensive comparative study is presented that demonstrates that PRIM II achieves results for the total cable length that are on average only 2.98% in excess of those obtained by the ILP benchmark. In addition, we apply our method, named FMM/ILP-based, to real-world cable path planning examples and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes.