Originating from the work of Navarro and Thankachan [TCS 2016], the problem of consecutive pattern matching is a variant of the fundamental pattern matching problem, where one is given a text and a pair of patterns, and must compute their consecutive occurrences in the text. Assuming that the text is given as a straight-line program, we develop an algorithm that computes all consecutive occurrences in optimal time.

Information extraction from textual data, where the query is represented by a finite transducer and the task is to enumerate all results without repetition, and its extension to the weighted case, where each output element has a weight and the output elements are to be enumerated sorted by their weights, are important and well studied problems in database theory. On the one hand, the first framework already covers the well-known case of regular document spanners, while the latter setting covers several practically relevant tasks that cannot be described in the unweighted setting. It is known that in the unweighted case this problem can be solved with linear time preprocessing O(|D|) and output-linear delay O(|s|) in data complexity, where D is the input data and s is the current output element. For the weighted case, Bourhis, Grez, Jachiet, and Riveros [ICDT 2021] recently designed an algorithm with linear time preprocessing, but the delay of O(|s| · log|D|) depends on the size of the data. We first show how to leverage the existing results on enumerating shortest paths to obtain a simple alternative algorithm with linear preprocessing and a delay of O(|s i | + min\ log i, log|D| ) for the i th output element s i (in data complexity); thus, substantially improving the previous algorithm. Next, we develop a technically involved rounding technique that allows us to devise an algorithm with linear time preprocessing and output-linear delay O(|s|) with high probability. To this end, we combine tools from algebra, high-dimensional geometry, and linear programming.

We describe a data structure that stores a strings in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data structures, such as compressed trees and graphs. We show that our data structure can be built in a scalable manner and is both small and fast in practice compared to other data structures supporting such queries.