AWLCO: All-Window Length Co-Occurrence

TL;DR

This paper introduces AWLCO, an efficient online algorithm for analyzing co-occurrences in sequences across all window lengths, with applications in text, programming, and genomics, offering improved time and space complexity.

Contribution

The paper presents AWLCO, a novel online algorithm for all-window-length co-occurrence analysis with reduced complexity, and generalizes it for pattern analysis.

Findings

AWLCO computes co-occurrences in a single pass with expected O(n) time.

The algorithm achieves space complexity of O(√(n|I|)).

It extends to pattern analysis with expected O(n|I|) time.

Abstract

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 $O(n^2)$ 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 expected time complexity of $O(n)$ and space complexity of $O( \sqrt{ n|I| })$. Following this, we generalize our use case to patterns in which we propose an algorithm that computes all-window-length co-occurrence with expected time complexity $O(n|I|)$ and space complexity $O( \sqrt{n|I|} + e_{max}|I|)$, where $e_{max}$ is the length of the largest pattern.