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

Lightweight Lempel-Ziv Parsing

We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d >= 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to lightweight LZ77 factorization. Extensive experiments show that the new algorithm is superior in most cases, particularly at the lowest memory levels and for highly repetitive data. As a part of the algorithm, we describe new methods for computing matching statistics which may be of independent interest.Comment: 12 page

Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page

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

String Indexing with Compressed Patterns

Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is given in compressed form and the goal is to achieve query time that is fast in terms of the compressed size of the pattern. This captures the common client-server scenario, where a client submits a query and communicates it in compressed form to a server. Instead of the server decompressing the query before processing it, we consider how to efficiently process the compressed query directly. Our main result is a novel linear space data structure that achieves near-optimal query time for patterns compressed with the classic Lempel-Ziv 1977 (LZ77) compression scheme. Along the way we develop several data structural techniques of independent interest, including a novel data structure that compactly encodes all LZ77 compressed suffixes of a string in linear space and a general decomposition of tries that reduces the search time from logarithmic in the size of the trie to logarithmic in the length of the pattern

Rank, select and access in grammar-compressed strings

Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the following operations on a grammar-compressed string: \mbox{rank}_c(S,i) (return the number of occurrences of symbol $c$ before position $i$ in $S$); \mbox{select}_c(S,i) (return the position of the $i$th occurrence of $c$ in $S$); and \mbox{access}(S,i,j) (return substring $S[i,j]$). For rank and select we describe data structures of size $O(n\sigma\log N)$ bits that support the two operations in $O(\log N)$ time. We propose another structure that uses $O(n\sigma\log (N/n)(\log N)^{1+\epsilon})$ bits and that supports the two queries in $O(\log N/\log\log N)$, where $\epsilon>0$ is an arbitrary constant. To our knowledge, we are the first to study the asymptotic complexity of rank and select in the grammar-compressed setting, and we provide a hardness result showing that significantly improving the bounds we achieve would imply a major breakthrough on a hard graph-theoretical problem. Our main result for access is a method that requires $O(n\log N)$ bits of space and $O(\log N+m/\log_\sigma N)$ time to extract $m=j-i+1$ consecutive symbols from $S$. Alternatively, we can achieve $O(\log N/\log\log N+m/\log_\sigma N)$ query time using $O(n\log (N/n)(\log N)^{1+\epsilon})$ bits of space. This matches a lower bound stated by Verbin and Yu for strings where $N$ is polynomially related to $n$.Comment: 16 page

Rpair: Rescaling RePair with Rsync

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 internal memory. Even then, however, the scheme is essentially useless unless it can be built on the original dataset reasonably quickly while keeping the dataset on disk. In this paper we show how we can preprocess such datasets with context-triggered piecewise hashing such that afterwards we can apply RePair and other grammar-based compressors more easily. We first give our algorithm, then show how a variant of it can be used to approximate the LZ77 parse, then leverage that to prove theoretical bounds on compression, and finally give experimental evidence that our approach is competitive in practice