arXiv subjects

Gonzalo Navarro

Publications and source records attributed to Gonzalo Navarro.

132 records · Page 8Linked to original sources

arXiv2010

New Algorithms on Wavelet Trees and Applications to Information Retrieval

Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the virtues of this versatile data structure. In particular we show how to use wavelet trees to solve fundamental algorithmic problems such as {\em range quantile} queries, {\em range next value} queries, and {\em range intersection} queries. We explore several applications of these queries in Information Retrieval, in particular {\em document retrieval} in hierarchical and temporal documents, and in the representation of {\em inverted lists}.

cs.DS↗

arXiv2010

Fully-Functional Static and Dynamic Succinct Trees

We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in constant time under the word-RAM model. However the data structures are complicated and difficult to dynamize. We propose a simple and flexible data structure, called the range min-max tree, that reduces the large number of relevant tree operations considered in the literature to a few primitives that are carried out in constant time on sufficiently small trees. The result is extended to trees of arbitrary size, achieving $2n + O(n /\polylog(n))$ bits of space. The redundancy is significantly lower than any previous proposal. Our data structure builds on the range min-max tree to achieve $2n+O(n/\log n)$ bits of space and $O(\log n)$ time for all the operations. We also propose an improved data structure using $2n+O(n\log\log n/\log n)$ bits and improving the time to the optimal $O(\log n/\log \log n)$ for most operations. Furthermore, we support sophisticated operations that allow attaching and detaching whole subtrees, in time $\Order(\log^{1+ε} n / \log\log n)$. Our techniques are of independent interest. One allows representing dynamic bitmaps and sequences supporting rank/select and indels, within zero-order entropy bounds and optimal time $O(\log n / \log\log n)$ for all operations on bitmaps and polylog-sized alphabets, and $O(\log n \log σ/ (\log\log n)^2)$ on larger alphabet sizes $σ$. This improves upon the best existing bounds for entropy-bounded storage of dynamic sequences, compressed full-text self-indexes, and compressed-space construction of the Burrows-Wheeler transform.

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arXiv2009

Re-Pair Compression of Inverted Lists

Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers. In this paper we explore a completely different alternative: We use Re-Pair compression of those differences. While Re-Pair by itself offers fast decompression at arbitrary positions in main and secondary memory, we introduce variants that in addition speed up the operations required for inverted list intersection. We compare the resulting data structures with several recent proposals under various list intersection algorithms, to conclude that our Re-Pair variants offer an interesting time/space tradeoff for this problem, yet further improvements are required for it to improve upon the state of the art.

cs.IR↗

arXiv2009

Fast and Compact Prefix Codes

It is well-known that, given a probability distribution over $n$ characters, in the worst case it takes (Θ(n \log n)) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for any $0<ε<1/2$ with (1 / ε= \Oh{\polylog{n}}), it takes $\Oh{n \log \log (1 / ε)}$ bits to store a prefix code with expected codeword length within $ε$ of the minimum. We then show that, for any constant (c > 1), it takes $\Oh{n^{1 / c} \log n}$ bits to store a prefix code with expected codeword length at most $c$ times the minimum. In both cases, our data structures allow us to encode and decode any character in $\Oh{1}$ time.

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arXiv2009

Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $π$ over n integers, taking advantage of ordered subsequences in $π$, while supporting its application $π$(i) and the application of its inverse $π^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $π^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays.

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arXiv2007

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.

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