## 2 Related Works
Within this domain, the authors of [26] present a linear programming problem to address service provision and resource allocation challenges in a Low Earth Orbit (LEO) network, with the objective to minimize the utilization of Inter-Satellite Links (ISLs) due to their inherent instability. Building on similar challenges, ref. [27] investigates satellite edge computing (SEC) as a paradigm that integrates Mobile Edge Computing (MEC) with satellite-terrestrial networks, leveraging LEO satellites as edge servers to reduce latency. Specifically, the authors formulate a delay-aware service-chaining problem in which Virtualized Network Functions (VNFs) must be optimally placed on LEO satellites and traffic routes selected to minimize the end-to-end delay. They propose both an approximation algorithm for single-request scenarios and an online algorithm for dynamic environments with uncertain delays, demonstrating improved latency performance through their SEC framework. Recently, there is an increasing interest in the application of mega-constellations, potentially endowed with on-board processing capability, to support EO. In particular, the \(\Phi\)-Sat-1 Mission [9] by the European Space Agency demonstrated possibility of processing data on board of EO satellite to select and downlink useful information only by applying AI techniques, moving the next research frontier to the investigation on leveraging the combination of networks made by a high number of satellites in mega-constellations and the possibility to process data on board. Under this point of view, the authors of [28] introduced a solution to obtain lower EO data delivery latency by taking advantage of mega-constellations, while the authors of [13] improved the timeliness of EO data by leveraging load balancing in EO constellations endowed with in-orbit processing capability. Instead, the authors of [29] presented an optimal strategy to jointly allocate resource and place processing in satellite networks dedicated to EO with the aim of minimizing a total operating cost related to the transmission, processing, and storage of data. Another highly investigated aspect is related to machine learning techniques applied in this orbital scenario. In particular, the authors of [30] give a state-of-the-art presentation on federated techniques in mega-LEO constellations, a topic also investigated in papers [12; 31; 32] focusing on different strategies to improve the in-orbit training of machine learning to be applied to EO. In a similar direction, ref. [33] proposes a two-timescale optimization framework that combines service deployment and task scheduling in satellite edge computing, using a deep reinforcement learning approach to improve energy efficiency, load balancing, and delay performance while controlling deployment overhead through heuristic techniques. Whereas, in our previous work [34], we propose a communication strategy to enable a fully distributed learning approach for training a deep learning model in orbit, taking advantage of the potential formation of a satellite network through the availability of ISLs within and across orbital planes. Finally, since on-board data processing requires energy, the authors of [18] propose an algorithm to minimize the energy consumption on satellites while guaranteeing desired latency, while the algorithm proposed by authors of [35] aims at optimizing the use of satellite batteries to extend their operation life. However, this may lead to an increased latency in service processing, at the expense of possible requirements on the Quality of Service in terms of timeliness. Additionally, ref. [36] proposes a hardware-level solution based on Stacked Intelligent Metasurfaces (SIM) to reduce energy consumption on LEO satellites by enabling lightweight, low-power beamforming directly in the electromagnetic domain, thus alleviating the computational load of traditional processing schemes.