Data Structures A Locally Adaptive Data

Communications of the ACM, 1986

A data compression scheme that exploits locality of reference, such as occurs when words are used frequently over short intervals and then fall into long periods of disuse, is described. The scheme is based on a simple heuristic for self-organizing sequential search and on variable-length encodings of integers. We prove that it never performs much worse than Huffman coding and can perform substantially better; experiments on real files show that its performance is usually quite close to that of Huffman coding. Our scheme has many implementation advantages: it is simple, allows fast encoding and decoding, and requires only one pass over the data to be compressed (static Huffman coding takes two passes).

A data compression scheme that exploits locality of reference, such as occurs when words are used frequently over short intervals and then fall into long periods of disuse, is described. The scheme is based on a simple heuristic for self-organizing sequential search and on variable-length encodings of integers. We prove that it never performs much worse than Huffman coding and can perform substantially better; experiments on real files show that its performance is usually quite close to that of Huffman coding. Our scheme has many implementation advantages: it is simple, allows fast encoding and decod- ing, and requires only one pass over the data to be com- pressed (static Huffman coding takes huo passes).

The Computer Journal, 2011

Semistatic word-based byte-oriented compressors are known to be attractive alternatives to compress natural language texts. With compression ratios around 30-35%, they allow fast direct searching of compressed text. In this article we reveal that these compressors have even more benefits. We show that most of the state-of-the-art compressors benefit from compressing not the original text, but the compressed representation obtained by a word-based byte-oriented statistical compressor. For example, p7zip with a dense-coding preprocessing achieves even better compression ratios and much faster compression than p7zip alone. We reach compression ratios below 17% in typical large English texts, which was obtained only by the slow PPM compressors. Furthermore, searches perform much faster if the final compressor operates over word-based compressed text. We show that typical self-indexes also profit from our preprocessing step. They achieve much better space and time performance when indexing is preceded by a compression step. Apart from using the well-known Tagged Huffman code, we present a new suffix-free Dense-Code-based compressor that compresses slightly better. We also show how some self-indexes can handle non-suffix-free codes. As a result, the compressed/indexed text requires around 35% of the space of the original text and allows indexed searches for both words and phrases.

2011

Efficient access to large data collections is nowadays an interesting problem for many research areas and applications. A recent conception of the time-space relationship suggests a strong relation between data compression and algorithms in the comparison model. In this sense, efficient algorithms could be used to induce compressed representations of the data they process. Examples of this relationship include unbounded search algorithms and integer encodings, adaptive sorting algorithms and compressed representation of permutations, or union algorithms and encoding for bit vectors. In this thesis, we propose to study the time-space relationship on different data types. We aim to define new compression schemes and compressed data structures based on adaptive algorithms that work over these data types, and to evaluate their practicality in data compression applications.

Theoretical Computer Science, 2019

The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family of techniques that exploits text repetitions in different ways. For each such compression scheme, several different indexing solutions have been proposed in the last two decades. To date, the fastest indexes for repetitive texts are based on the run-length compressed Burrows-Wheeler transform (BWT) and on the Compact Directed Acyclic Word Graph (CDAWG). The most space-efficient indexes, on the other hand, are based on the Lempel-Ziv parsing and on grammar compression. Indexes for more universal schemes such as collage systems and macro schemes have not yet been proposed. Very recently, Kempa and Prezza [STOC 2018] showed that all dictionary compressors can be interpreted as approximation algorithms for the smallest string attractor, that is, a set of text positions capturing all distinct substrings. Starting from this observation, in this paper we develop the first universal compressed self-index, that is, the first indexing data structure based on string attractors, which can therefore be built on top of any dictionary-compressed text representation. Let γ be the size of a string attractor for a text of length n. From known reductions, γ can be chosen to be asymptotically equal to any repetitiveness measure: number of runs in the BWT, size of the CDAWG, number of Lempel-Ziv phrases, number of rules in a grammar or collage system, size of a macro scheme. Our index takes O(γ lg(n/γ)) words of space and supports locating the occ occurrences of any pattern of length m in O(m lg n + occ lg n) time, for any constant > 0. This is, in particular, the first index for general macro schemes and collage systems. Our result shows that the relation between indexing and compression is much deeper than what was previously thought: the simple property standing at the core of all dictionary compressors is sufficient to support fast indexed queries.

Fundamenta Informaticae, 2011

Self-indexes aim at representing text collections in a compressed format that allows extracting arbitrary portions and also offers indexed searching on the collection. Current self-indexes are unable of fully exploiting the redundancy of highly repetitive text collections that arise in several applications. Grammar-based compression is well suited to exploit such repetitiveness. We introduce the first grammar-based self-index. It builds on Straight-Line Programs (SLPs), a rather general kind of context-free grammars. If an SLP of n rules represents a text T [1, u], then an SLP-compressed representation of T requires 2n log 2 n bits. For that same SLP, our self-index takes O(n log n) + n log 2 u bits. It extracts any text substring of length m in time O((m + h) log n), and finds occ occurrences of a pattern string of length m in time O((m(m + h) + h occ) log n), where h is the height of the parse tree of the SLP. No previous grammar representation had achieved o(n) search time. As byproducts we introduce (i) a representation of SLPs that takes 2n log 2 n(1 + o(1)) bits and efficiently supports more operations than a plain array of rules; (ii) a representation for binary relations with labels supporting various extended queries; (iii) a generalization of our self-index to grammar compressors that reduce T to a sequence of terminals and nonterminals, such as Re-Pair and LZ78.

Lecture Notes in Computer Science, 2009

offer powerful text compression by representing a text T [1, u] in terms of a restricted context-free grammar of n rules, so that T can be recovered in O(u) time. However, the problem of operating the grammar in compressed form has not been studied much. We present a grammar representation whose size is of the same order of that of a plain SLP representation, and can answer other queries apart from expanding nonterminals. This can be of independent interest. We then extend it to achieve the first grammar representation able of extracting text substrings, and of searching the text for patterns, in time o(n). We also give byproducts on representing binary relations.

Software: Practice and Experience, 2008

Semistatic byte-oriented word-based compression codes have been shown to be an attractive alternative to compress natural language text databases, because of the combination of speed, effectiveness, and direct searchability they offer. In particular, our recently proposed family of dense compression codes has been shown to be superior to the more traditional byte-oriented word-based Huffman codes in most aspects. In this paper, we focus on the problem of transmitting texts among peers that do not share the vocabulary. This is the typical scenario for adaptive compression methods. We design adaptive variants of our semistatic dense codes, showing that they are much simpler and faster than dynamic Huffman codes and reach almost the same compression effectiveness. We show that our variants have a very compelling trade-off between compression/decompression speed, compression ratio and search speed compared with most of the state-of-the-art general compressors.

Information Processing Letters, 2006

1992

Data may be compressed using textual substitution. Textual substitution identifies repeated substrings and replaces some or all substrings by pointers to another copy. We construct an incremental algorithm for a specific textual substitution method: coding a text with respect to a dictionary. With this incremental algorithm it is possible to combine two coded texts in constant time.