摘要：Analyzing patterns in a sequence of events has applications in text analysis, computer programming, and genomics research. In this paper, we consider the all-window-length analysis model which analyzes a sequence of events with respect to windows of all lengths. We study the exact co-occurrence counting problem for the all-window-length analysis model. Our first algorithm is an offline algorithm that counts all-window-length co-occurrences by performing multiple passes over a sequence and computing single-window-length co-occurrences. This algorithm has the time complexity O(n) for each window length and thus a total complexity of O(n²) and the space complexity O( I ) for a sequence of size n and an itemset of size I . We propose AWLCO, an online algorithm that computes all-window-length co-occurrences in a single pass with the time complexity of O(n) and space complexity of O(â^S{n I }), assuming perfect hashing. Following this, we generalize our use case to patterns in which we propose an algorithm that computes all-window-length co-occurrence with time complexity O(n I ), assuming perfect hashing, with an additional pre-processing step and space complexity O(â^S{n I } I ), plus the overhead of the Aho-Corasick algorithm [Aho and Corasick, 1975].
