{'fraction_non_alphanumeric': 0.024518388791593695, 'fraction_numerical': 0.0070052539404553416, 'mean_word_length': 4.553398058252427, '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 Prize-collecting Call Control Problem on Weighted Lines and Rings

Given a set of request calls with different demands and penalty costs, the prize-collecting call control (PCCC) problem is to minimize the sum of the maximum load on the edges and the total penalty cost of the rejected calls. In this paper, we prove that the PCCC problem on weighted lines is NP -hard even for special cases, and design a 1.582-approximation algorithm using a randomized rounding technique. In addition, we consider some special cases of the PCCC problem on weighted lines and rings.