Improved algorithms for string searching problems

We present improved practically efficient algorithms for several string searching problems, where we search for a short string called the pattern in a longer string called the text. We are mainly interested in the online problem, where the text is not preprocessed, but we also present a light indexing approach to speed up exact searching of a single pattern. The new algorithms can be applied e.g. to many problems in bioinformatics and other content scanning and filtering problems. In addition to exact string matching, we develop algorithms for several other variations of the string matching problem. We study algorithms for approximate string matching, where a limited number of errors is allowed in the occurrences of the pattern, and parameterized string matching, where a substring of the text matches the pattern if the characters of the substring can be renamed in such a way that the renamed substring matches the pattern exactly. We also consider searching multiple patterns simultaneously and searching weighted patterns, where the weight of a character at a given position reflects the probability of that character occurring at that position. Many of the new algorithms use the backward matching principle, where the characters of the text that are aligned with the pattern are read backward, i.e. from right to left. Another common characteristic of the new algorithms is the use of q-grams, i.e. q consecutive characters are handled as a single character. Many of the new algorithms are bit parallel, i.e. they pack several variables to a single computer word and update all these variables with a single instruction. We show that the q-gram backward string matching algorithms that solve the exact, approximate, or multiple string matching problems are optimal on average. We also show that the q-gram backward string matching algorithm for the parameterized string matching problem is sublinear on average for a class of moderately repetitive patterns. All the presented algorithms are also shown to be fast in practice when compared to earlier algorithms. We also propose an alphabet sampling technique to speed up exact string matching. We choose a subset of the alphabet and select the corresponding subsequence of the text. String matching is then performed on this reduced subsequence and the found matches are verified in the original text. We show how to choose the sampled alphabet optimally and show that the technique speeds up string matching especially for moderate to long patterns

A Bloom filter based semi-index on qq-grams

We present a simple $q$-gram based semi-index, which allows to look for a pattern typically only in a small fraction of text blocks. Several space-time tradeoffs are presented. Experiments on Pizza & Chili datasets show that our solution is up to three orders of magnitude faster than the Claude et al. \cite{CNPSTjda10} semi-index at a comparable space usage

Prospects and limitations of full-text index structures in genome analysis

The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared

Compressed Text Indexes:From Theory to Practice!

A compressed full-text self-index represents a text in a compressed form and still answers queries efficiently. This technology represents a breakthrough over the text indexing techniques of the previous decade, whose indexes required several times the size of the text. Although it is relatively new, this technology has matured up to a point where theoretical research is giving way to practical developments. Nonetheless this requires significant programming skills, a deep engineering effort, and a strong algorithmic background to dig into the research results. To date only isolated implementations and focused comparisons of compressed indexes have been reported, and they missed a common API, which prevented their re-use or deployment within other applications. The goal of this paper is to fill this gap. First, we present the existing implementations of compressed indexes from a practitioner's point of view. Second, we introduce the Pizza&Chili site, which offers tuned implementations and a standardized API for the most successful compressed full-text self-indexes, together with effective testbeds and scripts for their automatic validation and test. Third, we show the results of our extensive experiments on these codes with the aim of demonstrating the practical relevance of this novel and exciting technology

The Swap Matching Problem Revisited

In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using the model, we devise two efficient algorithms to solve the swap matching problem. The resulting algorithms are adaptations of the classic shift-and algorithm. For patterns having length similar to the word-size of the target machine, both the algorithms run in linear time considering a fixed alphabet.Comment: 23 pages, 3 Figures and 17 Table