Gonzalo Navarro

Gonzalo Navarro
University of Chile · Departamento de Ciencias de la Computación

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438
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Publications

Publications (438)
Article
Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using O(1) bits per node can break this bound on clustered point sets, while offering efficient range searches. We then describe a new compact quadtree representation based on heavy-pa...
Article
We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of m edges within 4m bits, which is close to the information-theoretic lower bound of about 3.58m. With 4m+o(m) bits of spa...
Article
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless compression scheme for real-valued matrices which achieves efficient performance in terms of compression ratio and t...
Article
Full-text available
Computing the product of the (binary) adjacency matrix of a large graph with a real-valued vector is an important operation that lies at the heart of various graph analysis tasks, such as computing PageRank. In this paper, we show that some well-known webgraph and social graph compression formats are computation-friendly, in the sense that they all...
Preprint
Full-text available
We present a new semi-external algorithm that builds the Burrows-Wheeler transform variant of Bauer et al. (a.k.a., BCR BWT) in linear expected time. Our method uses compression techniques to reduce the computational costs when the input is massive and repetitive. Concretely, we build on induced suffix sorting (ISS) and resort to run-length and gra...
Preprint
Full-text available
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless compression scheme for real-valued matrices which achieves efficient performance in terms of compression ratio and t...
Article
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality one e...
Article
For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in which codewords are assigned to symbols. In this paper we first show how, given a probability distribution over a...
Article
We address the problem of representing dynamic graphs using k2-trees. The k2-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact representations of bit vectors. Hence, by relying on compact representations of dynamic bit vectors, we can also repres...
Preprint
Full-text available
We introduce a time- and space-efficient technique to solve regularpath queries over labeled graphs. We combine a bit-parallel simula-tion of the Glushkov automaton of the regular expression with thering index introduced by Arroyuelo et al., exploiting its wavelettree representation of the triples in order to efficiently reach thestates of the prod...
Preprint
We propose a new representation of the offsets of the Lempel-Ziv (LZ) factorization based on the co-lexicographic order of the processed prefixes. The selected offsets tend to approach the k-th order empirical entropy. Our evaluations show that this choice of offsets is superior to the rightmost LZ parsing and the bit-optimal LZ parsing on datasets...
Preprint
Full-text available
In this systems paper, we present MillenniumDB: a novel graph database engine that is modular, persistent, and open source. MillenniumDB is based on a graph data model, which we call domain graphs, that provides a simple abstraction upon which a variety of popular graph models can be supported. The engine itself is founded on a combination of tried...
Article
Full-text available
The Lempel-Ziv 78 ( LZ78 ) and Lempel-Ziv-Welch ( LZW ) text factorizations are popular, not only for bare compression but also for building compressed data structures on top of them. Their regular factor structure makes them computable within space bounded by the compressed output size. In this article, we carry out the first thorough study of low...
Chapter
A grammar self-index of a text T (Claude et al. 2012) consists of a grammar \({\mathcal {G}}\) that only produces T and a geometric data structure that indexes the string cuts of the right-hand sides of \({\mathcal {G}}\)’s rules. This representation uses space proportional to G, the size of the grammar, which is small when the text is repetitive....
Article
Full-text available
Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks us to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative frequencies in that range are more than a threshold $\tau$. Subsequent authors have reduced their time and sp...
Article
Let a text T[1..n] be the only string generated by a context-free grammar with g (terminal and nonterminal) symbols, and of size G (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a grammar-compressed representation of T, can be encoded using Glg⁡G bits. We introduce the first grammar-compressed inde...
Article
Let string S[1..n] be parsed into z phrases by the Lempel-Ziv algorithm. The corresponding compression algorithm encodes S in O(z) space, but it does not support random access to S. We introduce a data structure, the block tree, that represents S in O(zlog⁡(n/z)) space and extracts any symbol of S in time O(log⁡(n/z)), among other space-time tradeo...
Conference Paper
Computing the matching statistics of patterns with respect to a text is a fundamental task in bioinformatics, but a formidable one when the text is a highly compressed genomic database. Bannai et al. gave an efficient solution for this case, which Rossi et al. recently implemented, but it uses two passes over the patterns and buffers a pointer for...
Article
Compressing real-world graphs has many benefits such as improving or enabling the visualization in small memory devices, graph query processing, community search, and mining algorithms. This work proposes a novel compact representation for real sparse and clustered undirected graphs. The approach lists all the maximal cliques by using a fast algori...
Chapter
Prefix-free parsing (PFP) was introduced by Boucher et al. (2019) as a preprocessing step to ease the computation of Burrows-Wheeler Transforms (BWTs) of genomic databases. Given a string S, it produces a dictionary D and a parse P of overlapping phrases such that BWT(S) can be computed from D and P in time and workspace bounded in terms of their c...
Article
We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result, we combine several recent findings, including string attractors —new combinatorial objects encompassing most known compressibility measures for highly...
Chapter
Unlike in statistical compression, where Shannon’s entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures like the size z of the Lempel–Ziv parse are frequently used to estimate repetitiveness. Recently, a more prin...
Preprint
Full-text available
A grammar compression algorithm, called GCIS, is introduced in this work. GCIS is based on the induced suffix sorting algorithm SAIS, presented by Nong et al. in 2009. The proposed solution builds on the factorization performed by SAIS during suffix sorting. A context-free grammar is used to replace factors by non-terminals. The algorithm is then r...
Preprint
Computing the matching statistics of patterns with respect to a text is a fundamental task in bioinformatics, but a formidable one when the text is a highly compressed genomic database. Bannai et al. gave an efficient solution for this case, which Rossi et al. recently implemented, but it uses two passes over the patterns and buffers a pointer for...
Article
As the number of vehicles and devices equipped with GPS technology has grown explosively, an urgent need has arisen for time- and space-efficient data structures to represent their trajectories. The most commonly desired queries are the following: queries about an object’s trajectory, range queries, and nearest neighbor queries. In this paper, we c...
Article
Full-text available
Lempel–Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts. However, the existing efficient methods computing the exact LZ parsing have to use linear or close to linear space to index the input text during the construction of the parsing, which is prohibitive for long inputs. An alternative is Re...
Preprint
In recent years, RDF has gained popularity as a format for the standardized publication and exchange of information in the Web of Data. In this paper we introduce RDFCSA, a data structure that is able to self-index an RDF dataset in small space and supports efficient querying. RDFCSA regards the triples of the RDF store as short circular strings an...
Chapter
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as genomic databases. In a recent paper (SPIRE 2019) we showed how simple pre-processing can dramatically improve...
Chapter
The research on indexing repetitive string collections has focused on the same search problems used for regular string collections, though they can make little sense in this scenario. For example, the basic pattern matching query “list all the positions where pattern P appears” can produce huge outputs when P appears in an area shared by many docum...
Article
Full-text available
In the range α-majority query problem, we are given a sequence S[1…n] and a fixed threshold α∈(0,1), and are asked to preprocess S such that, given a query range [i…j], we can efficiently report the symbols that occur more than α(j-i+1) times in S[i…j], which are called the range α-majorities. In this article we describe the first compressed dynami...
Preprint
Prefix-free parsing (PFP) was introduced by Boucher et al. (2019) as a preprocessing step to ease the computation of Burrows-Wheeler Transforms (BWTs) of genomic databases. Given a string $S$, it produces a dictionary $D$ and a parse $P$ of overlapping phrases such that $\mathrm{BWT} (S)$ can be computed from $D$ and $P$ in time and workspace bound...
Article
We present the first solution to finding τ-majorities on tree paths. Given a tree of n nodes, each with a label from [1..σ], and a fixed threshold 0<τ<1, such a query gives two nodes u and v and asks for all the labels that appear more than τ⋅|Puv| times in the path Puv from u to v, where |Puv| denotes the number of nodes in Puv. Note that the answ...
Preprint
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through applications like bioinformatics, the string collections experienced a growth that outperforms Moore's Law and challe...
Preprint
Lempel-Ziv is an easy-to-compute member of a wide family of so-called macro schemes; it restricts pointers to go in one direction only. Optimal bidirectional macro schemes are NP-complete to find, but they may provide much better compression on highly repetitive sequences. We consider the problem of approximating optimal bidirectional macro schemes...
Conference Paper
Full-text available
We address the problem of representing dynamic graphs using k²-trees. The k²-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact representations of bit vectors. Hence, by relying on compact representations of dynamic bit vectors, we can also repres...
Preprint
We present a compact data structure to represent both the duration and length of homogeneous segments of trajectories from moving objects in a way that, as a data warehouse, it allows us to efficiently answer cumulative queries. The division of trajectories into relevant segments has been studied in the literature under the topic of Trajectory Segm...
Preprint
Full-text available
Signaling pathways are responsible for the regulation of cell processes, such as monitoring the external environment, transmitting information across membranes, and making cell fate decisions. Given the increasing amount of biological data available and the recent discoveries showing that many diseases are related to the disruption of cellular sign...
Article
There are many representations of planar graphs, but few are as elegant as Turán's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main disadvantage has been that “it does not allow efficient searching” (Jacobson, 1989). In this paper we show how to add...
Article
Indexing highly repetitive texts—such as genomic databases, software repositories and versioned text collections—has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is r , the number of runs in their Burrows-Wheeler Transforms (BWTs). One of the earliest indexes for repetitive co...
Preprint
Full-text available
This work introduces a companion reproducible paper with the aim of allowing the exact replication of the methods, experiments, and results discussed in a previous work [5]. In that parent paper, we proposed many and varied techniques for compressing indexes which exploit that highly repetitive collections are formed mostly of documents that are ne...
Preprint
Full-text available
We show that the topological model, a semantically rich standard to represent GIS data, can be encoded succinctly while efficiently answering a number of topology-related queries. We build on recent succinct planar graph representations so as to encode a model with $m$ edges within $4m+o(m)$ bits and answer various queries relating nodes, edges, an...
Preprint
Full-text available
The $k^2$-tree is a successful compact representation of binary relations that exhibit sparseness and/or clustering properties. It can be extended to $d$ dimensions, where it is called a $k^d$-tree. The representation boils down to a long bitvector. We show that interpreting the $k^d$-tree as a dynamic trie on the Morton codes of the points, instea...
Preprint
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly repetitive sequences, and classical statistical compression proves ineffective. We introduce, instead, grammar-based r...
Preprint
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix computation in suffix arrays. Our data structures yield relevant space-time tradeoffs in real-world dictionaries. We f...
Preprint
The raster model is commonly used for the representation of images in many domains, and is especially useful in Geographic Information Systems (GIS) to store information about continuous variables of the space (elevation, temperature, etc.). Current representations of raster data are usually designed for external memory or, when stored in main memo...
Preprint
We present Dv2v, a new dynamic (one-pass) variable-to-variable compressor. Variable-to-variable compression aims at using a modeler that gathers variable-length input symbols and a variable-length statistical coder that assigns shorter codewords to the more frequent symbols. In Dv2v, we process the input text word-wise to gather variable-length sym...
Preprint
We introduce a compressed data structure for the storage of free trajectories of moving objects (such as ships and planes) that efficiently supports various spatio-temporal queries. Our structure, dubbed GraCT, stores the absolute positions of all the objects at regular time intervals (snapshots) using a $k^2$-tree, which is a space- and time-effic...
Preprint
We address the problem of representing dynamic graphs using $k^2$-trees. The $k^2$-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact representations of bit vectors. Hence, by relying on compact representations of dynamic bit vectors, we can also...
Conference Paper
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix computation in suffix arrays. Our data structures yield relevant space-time tradeoffs in real-world dictionaries. We f...
Preprint
Shape grammars are well known in the graphics and design communities but are not such a common tool for researchers working in bioinformatics, data compression, data structures or formal languages. We are now investigating how to use shape grammars for the parse trees of straight-line programs (SLPs) to reduce the space needed to support random acc...
Preprint
Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such a clear measure exists for the compressibility of repetitive sequences other than the uncomputable Kolmogorov's complexity. Since statistical entropy does not capture repetitiveness, ad-hoc measures like the size $z$ of the Lempel-Ziv parse are frequentl...
Chapter
The \(k^2\)-tree is a successful compact representation of binary relations that exhibit sparseness and/or clustering properties. It can be extended to d dimensions, where it is called a \(k^d\)-tree. The representation boils down to a long bitvector. We show that interpreting the \(k^d\)-tree as a dynamic trie on the Morton codes of the points, in...
Chapter
Data compression is a powerful tool for managing massive but repetitive datasets, especially schemes such as grammar-based compression that support computation over the data without decompressing it. In the best case such a scheme takes a dataset so big that it must be stored on disk and shrinks it enough that it can be stored and processed in inte...
Chapter
We show that the topological model, a semantically rich standard to represent GIS data, can be encoded succinctly while efficiently answering a number of topology-related queries. We build on recent succinct planar graph representations so as to encode a model with m edges within \(4m+o(m)\) bits and answer various queries relating nodes, edges, an...
Article
Let D be a collection of string documents of n characters in total. The top-k document retrieval problem is to preprocess D into a data structure that, given a query (P,k), can return the k documents of D most relevant to pattern P. The relevance of a document d for a pattern P is given by a predefined ranking function w(P,d). Linear space and opti...
Article
The raster model is commonly used for the representation of images in many domains, and is especially useful in Geographic Information Systems (GIS) to store information about continuous variables of the space (elevation, temperature, etc.). Current representations of raster data are usually designed for external memory or, when stored in main memo...
Conference Paper
Full-text available
The k 2-tree is a successful compact representation of binary relations that exhibit sparseness and/or clustering properties. It can be extended to d dimensions, where it is called a k d-tree. The representation boils down to a long bitvector. We show that interpreting the k d-tree as a dynamic trie on the Morton codes of the points, instead of as...
Article
Full-text available
This work introduces a companion reproducible paper with the aim of allowing the exact replication of the methods, experiments, and results discussed in a previous work [5]. In that parent paper, we proposed many and varied techniques for compressing indexes which exploit that highly repetitive collections are formed mostly of documents that are ne...
Preprint
Data compression is a powerful tool for managing massive but repetitive datasets, especially schemes such as grammar-based compression that support computation over the data without decompressing it. In the best case such a scheme takes a dataset so big that it must be stored on disk and shrinks it enough that it can be stored and processed in inte...
Article
We introduce a compressed data structure for the storage of free trajectories of moving objects that efficiently supports various spatio-temporal queries. Our structure, dubbed GraCT, stores the absolute positions of all the objects at regular time intervals (snapshots) using a k²-tree, which is a space- and time-efficient region quadtree. Position...
Preprint
Full-text available
Lempel-Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts. However, the existing efficient methods computing the exact LZ parsing have to use linear or close to linear space to index the input text during the construction of the parsing, which is prohibitive for long inputs. An alternative is Re...
Preprint
Full-text available
Converting a set of sequencing reads into a lossless compact data structure that encodes all the relevant biological information is a major challenge. The classical approaches are to build the string graph or the de Bruijn graph. Each has advantages over the other depending on the application. Still, the ideal setting would be to have an index of t...
Preprint
String attractors are a novel combinatorial object encompassing most known compressibility measures for highly-repetitive texts. Recently, the first index building on an attractor of size $\gamma$ of a text $T[1..n]$ was obtained. It uses $O(\gamma\log(n/\gamma))$ space and finds the $occ$ occurrences of a pattern $P[1..m]$ in time $O(m\log n + occ...
Preprint
We present RCT, a new compact data structure to represent trajectories of objects. It is based on a relative compression technique called Relative Lempel-Ziv (RLZ), which compresses sequences by applying an LZ77 encoding with respect to an artificial reference. Combined with $O(z)$-sized data structures on the sequence of phrases that allows to sol...
Article
Let f:[1.n]→[1.n] be a function, and ℓ:[1.n]→[1.σ] indicate a label assigned to each element of the domain. We design several compact data structures that answer various kinds of summary queries on the labels of paths in f. For example, we can find either the minimum label in fk(i) for a given i and any k≥0 in a given range [k1.k2], or the minimum...
Preprint
Full-text available
Indexing highly repetitive texts --- such as genomic databases, software repositories and versioned text collections --- has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is $r$, the number of runs in their Burrows-Wheeler Transforms (BWTs). One of the earliest indexes for repe...
Preprint
Full-text available
We present the first solution to $\tau$-majorities on tree paths. Given a tree of $n$ nodes, each with a label from $[1..\sigma]$, and a fixed threshold $0<\tau<1$, such a query gives two nodes $u$ and $v$ and asks for all the labels that appear more than $\tau \cdot |P_{uv}|$ times in the path $P_{uv}$ from $u$ to $v$. Note that the answer to any...
Preprint
De novo DNA assembly is a fundamental task in Bioinformatics, and finding Eulerian paths on de Bruijn graphs is one of the dominant approaches to it. In most of the cases, there may be no one order for the de Bruijn graph that works well for assembling all of the reads. For this reason, some de Bruijn-based assemblers try assembling on several grap...