{'fraction_non_alphanumeric': 0.026920551543007223, 'fraction_numerical': 0.0006565988181221273, 'mean_word_length': 4.541818181818182, '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}}
An effective method to find the k shortest paths in a generalized time-window network

It is a challenging task to find the k shortest paths in a time-window network, where a node may have some specific time windows only within which is the node accessible. Existing research assumes that a traveller can pass through an accessible node immediately or wait to pass at start times of future time windows at the node. This paper targets at a more general case where a traveller, once arriving at a node, may choose to pass through the node at any discrete time in the time windows of the node. In such a generalized time-window network, the degree of complexity increases significantly, as the size of solution space soars up exponentially. By mimicking the natural ripple-spreading phenomenon on a liquid surface, we propose an effective ripple-spreading algorithm (RSA) for the k shortest paths problem in a generalized time-window network (k-SPPGTW). Besides one-to-one k-SPPGTW, the RSA is also extended to one-to-all k-SPPGTW, where all the k shortest paths from a given source to every other node in the network need to be found. The new method has a theoretical guarantee of optimality. The computational complexity of the reported RSA is just 0(k×NATU×NL), where Nl is the number of links in the network, and Natu is the average simulated time units for a ripple to travel through a link. The effectiveness and efficiency of the reported RSA for the k-SPPGTW are demonstrated by some preliminary experimental results.