{'fraction_non_alphanumeric': 0.017191977077363897, 'fraction_numerical': 0.0, 'mean_word_length': 5.781553398058253, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Time-Expanded Hypergraph Based Joint Heterogeneous Resource Representation and Scheduling in Satellite-Terrestrial Networks

As the spaceborne resources are heterogeneous and the satellite network topology changes constantly, various time-varying derivative graphs are designed to represent the data acquisition and delivery process in satellite-terrestrial integrated networks (STNs). However, the time complexity of resource allocation approaches based on assorted time-varying graphs is remaining obstinately exponential. Derived from the satellite vertical coverage feature, we design a more general relationship to involve a group of nodes in a hyperedge rather than the bilateral relationship between two nodes. In this paper, we propose a time-expanded hypergraph (TEH) to contract the adjacency matrix of the network topology. Based on the proposed TEH, the problem is formulated to minimize the consumption of the communication resource in the resource-limited STN while completing the same number of tasks. Since the problem is intractable by exhaustive search, we further propose a hybrid hyperedge and Lagrangian relaxation algorithm to perform optimal resource allocation through an oriented search for the feasible hyperedges to reduce the scale of searching. The simulation results validate that the proposed algorithm can effectively complete the tasks with lower time complexity.