# Dynamic Network Formation for FSO Satellite Communication
## 3 Minimum Spanning Tree on Dynamic Graphs (DMST)
### Discrete Dynamic Graphs \(Mst\)
Considering that the problem of finding the minimum bounded spanning tree is an NP-hard problem, a heuristic method for a cost-effective solution on a static graph was designed. This method searches for such a tree in a reasonable run-time. The main novelty of this work lies in the DBST method--this method provides a solution to the bounded degree spanning tree problem in a dynamic network that can also be used as a reasonable solution in real-time. Simulation experiments with real-world satellite data verify both the correctness and the efficiency of the algorithm. In the coming years, the size and complexity of LEO constellations (such as Starlink) is expected to grow dramatically, supporting millions of communication links [34]. Moreover, the overgrowing demand for reduced latency communication [35] raises several QoS (Quality of Service) routing problems, as some communication links are extremely sensitive to latency, while others can handle a relatively considerable delays. A natural future work may include generalizing the problem to be able to adjust to a dynamic communication demand. In this generalization, a large set of communication demands are presented as an offline (or online) ground-station to ground-station (peer2 peer) communication demands. The goal was to find the spanning graph that minimizes the weighted cost (or delay) over all the communication demands. In order to validate the performance of such a complicated (real-world) problem, there is a need to construct a detailed benchmark on which both online and offline methods can be evaluated. Having both the benchmark and the generalized methods, one should be able to compare \"Starlink-like\" solutions to existing fiber-optic solutions--which appears to be a major optimization problem related to 5G global networks. Conceptualization, R.M. and B.B.-M.; methodology, R.M., R.Y., T.G. and B.B.-M.; software, R.M. ; validation, R.Y., T.G. and B.B.-M.; formal analysis, T.G. ; investigation, R.M., R.Y., T.G. and B.B.-M.; writing--original draft preparation, R.M., R.Y., T.G. and B.B.-M.; writing--review and editing, R.M., T.G. and B.B.-M.; visualization, R.M. ; supervision, T.G. and B.B.-M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. ## References

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