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

TL;DR

This paper introduces a novel optimization method combining Fast Marching Method and Integer Linear Programming to design submarine cable networks with minimal cost while satisfying latency constraints, applicable to real-world scenarios.

Contribution

It presents a new integrated approach for constrained minimum spanning tree design in irregular 3D spaces, addressing NP-complete challenges with practical heuristics.

Findings

Effective cable path planning with latency constraints.

ILP approach is computationally feasible for most real systems.

Heuristic algorithm provides near-optimal solutions when ILP is too slow.

Abstract

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.