All-Time Dynamic Minimum Spanning Tree for Inter-Satellite Link Optimization in LEO Networks

The rapid expansion of Low Earth Orbit (LEO) satellite constellations presents new challenges for maintaining efficient inter-satellite communication under dynamic network topologies. Traditional minimum spanning tree (MST) algorithms, designed for static or quasi-static networks, are inefficient in handling frequent topology changes and fluctuating link costs in LEO environments. Moreover, existing dynamic MST approaches often rely on localized updates, which lack global foresight, resulting in scalability issues and poor real-time responsiveness. To address these challenges, we propose a novel time-varying topology model based on the inter-satellite link (ISL) properties and orbital prediction, introducing the concepts of Stable ISL Period (SIP) and Stable Communication Period (SCP) to identify intervals of topological stability. Building on this model, we develop the All-Time Dynamic Minimum Spanning Tree (ATDMST) algorithm, which incorporates a filtering mechanism to avoid unnecessary recomputations and employs an "edge swapping" strategy for incremental updates. The ATDMST algorithm dynamically maintains optimal spanning trees as ISL communication costs evolve, significantly reducing computational overhead while preserving communication efficiency. Evaluation results show that, that ATDMST outperforms existing methods, achieving up to an 8.8% reduction in communication costs, 95% fewer topology updates, and a 72% decrease in response time, while maintaining robust performance.