Large-scale low-Earth-orbit satellite constellations offer a promising platform for global low-latency networking, aided by faster propagation in free space than in fiber and copper. In such systems, end-to-end latency is largely determined by the inter-satellite link (ISL) topology. In particular, the network diameter, the maximum shortest path between any pair of satellites, serves as a key performance metric for time-sensitive applications. Designing diameter-optimal topologies is challenging due to degree constraints, line-of-sight limitations, and orbital dynamics. This paper proposes a two-stage optimization framework for ISL topology design. First, a continuous relaxation of the link selection problem is formulated as a convex program that maximizes the algebraic connectivity of the Laplacian, serving as a tractable surrogate for diameter minimization. Second, the resulting fractional solution is mapped to a feasible discrete topology using integer linear programming. An iterative local-search heuristic is also developed as a baseline. Extensive simulations on Walker-Delta constellations show that the proposed method consistently achieves smaller network diameters and improved robustness compared to conventional heuristics, while allowing trade-offs between latency and link persistence. The approach offers a principled framework for designing high-performance satellite mesh networks. For a constellation of 1,500 satellites, each equipped with four ISLs of up to 2,500 km, the network diameter can be reduced to as low as 12, yielding end-to-end delays under 90 ms between any two points on Earth.

翻译：大规模低轨卫星星座为全球低延迟组网提供了有前景的平台，这得益于自由空间中比光纤和铜线更快的传播速度。在此类系统中，端到端延迟主要由星间链路拓扑决定。具体而言，网络直径（任意卫星对之间最大最短路径）是时间敏感应用的关键性能指标。由于度约束、视线限制和轨道动力学的影响，设计直径最优的拓扑极具挑战性。本文提出了一种星间链路拓扑设计的两阶段优化框架。首先，将链路选择问题的连续松弛形式表述为一个凸优化问题，该问题最大化拉普拉斯矩阵的代数连通度，作为直径最小化的易于处理的替代目标。其次，利用整数线性规划将所得的分数解映射为可行的离散拓扑。此外，还开发了一种迭代局部搜索启发式方法作为基准。在Walker-Delta星座上的大量仿真表明，与传统启发式方法相比，所提方法始终能实现更小的网络直径和更强的鲁棒性，同时允许在延迟与链路持续性之间进行权衡。该方法为设计高性能卫星网状网络提供了一个原则性框架。对于一个包含1500颗卫星、每颗卫星配备四条最长2500公里星间链路的星座，网络直径可降至低至12，地球上任两点之间的端到端延迟可控制在90毫秒以内。