Negative Factor

The problem of finding matches of a regular expression (RE) on a string exists in many applications, such as text editing, biosequence search, and shell commands. Existing techniques first identify candidates using substrings in the RE, then verify each of them using an automaton. These techniques become inefficient when there are many candidate occurrences that need to be verified. In this article, we propose a novel technique that prunes false negatives by utilizing negative factors , which are substrings that cannot appear in an answer. A main advantage of the technique is that it can be integrated with many existing algorithms to improve their efficiency significantly. We present a detailed description of this technique. We develop an efficient algorithm that utilizes negative factors to prune candidates, then improve it by using bit operations to process negative factors in parallel. We show that negative factors, when used with necessary factors (substrings that must appear in each answer), can achieve much better pruning power. We analyze the large number of negative factors, and develop an algorithm for finding a small number of high-quality negative factors. We conducted a thorough experimental study of this technique on real datasets, including DNA sequences, proteins, and text documents, and show significant performance improvement of the state-of-the-art tools by an order of magnitude.