Universal Indexes for Highly Repetitive Document Collections

Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that are near-copies of others. Traditional techniques for indexing these collections fail to properly exploit their regularities in order to reduce space. We introduce new techniques for compressing inverted indexes that exploit this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar compression of the differential inverted lists, instead of the usual practice of gap-encoding them. We show that, in this highly repetitive setting, our compression methods significantly reduce the space obtained with classical techniques, at the price of moderate slowdowns. Moreover, our best methods are universal, that is, they do not need to know the versioning structure of the collection, nor that a clear versioning structure even exists. We also introduce compressed self-indexes in the comparison. These are designed for general strings (not only natural language texts) and represent the text collection plus the index structure (not an inverted index) in integrated form. We show that these techniques can compress much further, using a small fraction of the space required by our new inverted indexes. Yet, they are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

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

Document Retrieval on Repetitive Collections

Document retrieval aims at finding the most important documents where a pattern appears in a collection of strings. Traditional pattern-matching techniques yield brute-force document retrieval solutions, which has motivated the research on tailored indexes that offer near-optimal performance. However, an experimental study establishing which alternatives are actually better than brute force, and which perform best depending on the collection characteristics, has not been carried out. In this paper we address this shortcoming by exploring the relationship between the nature of the underlying collection and the performance of current methods. Via extensive experiments we show that established solutions are often beaten in practice by brute-force alternatives. We also design new methods that offer superior time/space trade-offs, particularly on repetitive collections.Comment: Accepted to ESA 2014. Implementation and experiments at http://www.cs.helsinki.fi/group/suds/rlcsa

Essential Incompleteness of Arithmetic Verified by Coq

A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural numbers, and functions operating on these codes are proved to be primitive recursive. The weak axiom system is proved to be essentially incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the associated Coq source files see the TeX sources, or see <http://r6.ca/Goedel20050512.tar.gz

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