{'fraction_non_alphanumeric': 0.02295552367288379, 'fraction_numerical': 0.0014347202295552368, 'mean_word_length': 4.915254237288136, '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}}
The Complexity of Finding Minimal Spanning Subgraphs

Let P be a property of graphs (directed or undirected). We consider the following problem: given a graph G that has property P, find a minimal spanning subgraph of G with property P. We describe an algorithm for this problem and prove that it is correct under some rather weak assumptions about P. We then analyze the number of iterations of this algorithm. By suitably restricting the graph properties, we devise a general technique to construct graphs for which the algorithm requires a large number of iterations. We apply the above technique to three concrete graph properties: 2-edge-connectivity, biconnectivity, and strong connectivity.