Random Access to Grammar Compressed Strings

Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string. Let $S$ be a string of length $N$ compressed into a context-free grammar $\mathcal{S}$ of size $n$. We present two representations of $\mathcal{S}$ achieving $O(\log N)$ random access time, and either $O(n\cdot \alpha_k(n))$ construction time and space on the pointer machine model, or $O(n)$ construction time and space on the RAM. Here, $\alpha_k(n)$ is the inverse of the $k^{th}$ row of Ackermann's function. Our representations also efficiently support decompression of any substring in $S$: we can decompress any substring of length $m$ in the same complexity as a single random access query and additional $O(m)$ time. Combining these results with fast algorithms for uncompressed approximate string matching leads to several efficient algorithms for approximate string matching on grammar-compressed strings without decompression. For instance, we can find all approximate occurrences of a pattern $P$ with at most $k$ errors in time $O(n(\min\{|P|k, k^4 + |P|\} + \log N) + occ)$, where $occ$ is the number of occurrences of $P$ in $S$. Finally, we generalize our results to navigation and other operations on grammar-compressed ordered trees. All of the above bounds significantly improve the currently best known results. To achieve these bounds, we introduce several new techniques and data structures of independent interest, including a predecessor data structure, two "biased" weighted ancestor data structures, and a compact representation of heavy paths in grammars.Comment: Preliminary version in SODA 201

간결한 자료구조를 활용한 반구조화된 문서 형식들의 공간 효율적 표현법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2021. 2. Srinivasa Rao Satti.Numerous big data are generated from a plethora of sources. Most of the data stored as files contain a non-fixed type of schema, so that the files are suitable to be maintained as semi-structured document formats. A number of those formats, such as XML (eXtensible Markup Language), JSON (JavaScript Object Notation), and YAML (YAML Ain't Markup Language) are suggested to sustain hierarchy in the original corpora of data. Several data models structuring the gathered data - including RDF (Resource Description Framework) - depend on the semi-structured document formats to be serialized and transferred for future processing. Since the semi-structured document formats focus on readability and verbosity, redundant space is required to organize and maintain the document. Even though general-purpose compression schemes are widely used to compact the documents, applying those algorithms hinder future handling of the corpora, owing to loss of internal structures. The area of succinct data structures is widely investigated and researched in theory, to provide answers to the queries while the encoded data occupy space close to the information-theoretic lower bound. Bit vectors and trees are the notable succinct data structures. Nevertheless, there were few attempts to apply the idea of succinct data structures to represent the semi-structured documents in space-efficient manner. In this dissertation we propose a unified, space-efficient representation of various semi-structured document formats. The core functionality of this representation is its compactness and query-ability derived from enriched functions of succinct data structures. Incorporation of (a) bit indexed arrays, (b) succinct ordinal trees, and (c) compression techniques engineers the compact representation. We implement this representation in practice, and show by experiments that construction of this representation decreases the disk usage by up to 60% while occupying 90% less RAM. We also allow processing a document in partial manner, to allow processing of larger corpus of big data even in the constrained environment. In parallel to establishing the aforementioned compact semi-structured document representation, we provide and reinforce some of the existing compression schemes in this dissertation. We first suggest an idea to encode an array of integers that is not necessarily sorted. This compaction scheme improves upon the existing universal code systems, by assistance of succinct bit vector structure. We show that our suggested algorithm reduces space usage by up to 44% while consuming 15% less time than the original code system, while the algorithm additionally supports random access of elements upon the encoded array. We also reinforce the SBH bitmap index compression algorithm. The main strength of this scheme is the use of intermediate super-bucket during operations, giving better performance on querying through a combination of compressed bitmap indexes. Inspired from splits done during the intermediate process of the SBH algorithm, we give an improved compression mechanism supporting parallelism that could be utilized in both CPUs and GPUs. We show by experiments that this CPU parallel processing optimization diminishes compression and decompression times by up to 38% in a 4-core machine without modifying the bitmap compressed form. For GPUs, the new algorithm gives 48% faster query processing time in the experiments, compared to the previous existing bitmap index compression schemes.셀 수 없는 빅 데이터가 다양한 원본로부터 생성되고 있다. 이들 데이터의 대부분은 고정되지 않은 종류의 스키마를 포함한 파일 형태로 저장되는데, 이로 인하여 반구조화된 문서 형식을 이용하여 파일을 유지하는 것이 적합하다. XML, JSON 및 YAML과 같은 종류의 반구조화된 문서 형식이 데이터에 내재하는 구조를 유지하기 위하여 제안되었다. 수집된 데이터를 구조화하는 RDF와 같은 여러 데이터 모델들은 사후 처리를 위한 저장 및 전송을 위하여 반구조화된 문서 형식에 의존한다. 반구조화된 문서 형식은 가독성과 다변성에 집중하기 때문에, 문서를 구조화하고 유지하기 위하여 추가적인 공간을 필요로 한다. 문서를 압축시키기 위하여 일반적인 압축 기법들이 널리 사용되고 있으나, 이들 기법들을 적용하게 되면 문서의 내부 구조의 손실로 인하여 데이터의 사후 처리가 어렵게 된다. 데이터를 정보이론적 하한에 가까운 공간만을 사용하여 저장을 가능하게 하면서 질의에 대한 응답을 제공하는 간결한 자료구조는 이론적으로 널리 연구되고 있는 분야이다. 비트열과 트리가 널리 알려진 간결한 자료구조들이다. 그러나 반구조화된 문서들을 저장하는 데 간결한 자료구조의 아이디어를 적용한 연구는 거의 진행되지 않았다. 본 학위논문을 통해 우리는 다양한 종류의 반구조화된 문서 형식을 통일되게 표현하는 공간 효율적 표현법을 제시한다. 이 기법의 주요한 기능은 간결한 자료구조가 강점으로 가지는 특성에 기반한 간결성과 질의 가능성이다. 비트열로 인덱싱된 배열, 간결한 순서 있는 트리 및 다양한 압축 기법을 통합하여 해당 표현법을 고안하였다. 이 기법은 실재적으로 구현되었고, 실험을 통하여 이 기법을 적용한 반구조화된 문서들은 최대 60% 적은 디스크 공간과 90% 적은 메모리 공간을 통해 표현될 수 있다는 것을 보인다. 더불어 본 학위논문에서 반구조화된 문서들은 분할적으로 표현이 가능함을 보이고, 이를 통하여 제한된 환경에서도 빅 데이터를 표현한 문서들을 처리할 수 있다는 것을 보인다. 앞서 언급한 공간 효율적 반구조화된 문서 표현법을 구축함과 동시에, 본 학위논문에서 이미 존재하는 압축 기법 중 일부를 추가적으로 개선한다. 첫째로, 본 학위논문에서는 정렬 여부에 관계없는 정수 배열을 부호화하는 아이디어를 제시한다. 이 기법은 이미 존재하는 범용 코드 시스템을 개선한 형태로, 간결한 비트열 자료구조를 이용한다. 제안된 알고리즘은 기존 범용 코드 시스템에 비해 최대 44\% 적은 공간을 사용할 뿐만 아니라 15\% 적은 부호화 시간을 필요로 하며, 기존 시스템에서 제공하지 않는 부호화된 배열에서의 임의 접근을 지원한다. 또한 본 학위논문에서는 비트맵 인덱스 압축에 사용되는 SBH 알고리즘을 개선시킨다. 해당 기법의 주된 강점은 부호화와 복호화 진행 시 중간 매개인 슈퍼버켓을 사용함으로써 여러 압축된 비트맵 인덱스에 대한 질의 성능을 개선시키는 것이다. 위 압축 알고리즘의 중간 과정에서 진행되는 분할에서 영감을 얻어, 본 학위논문에서 CPU 및 GPU에 적용 가능한 개선된 병렬화 압축 매커니즘을 제시한다. 실험을 통해 CPU 병렬 최적화가 이루어진 알고리즘은 압축된 형태의 변형 없이 4코어 컴퓨터에서 최대 38\%의 압축 및 해제 시간을 감소시킨다는 것을 보인다. GPU 병렬 최적화는 기존에 존재하는 GPU 비트맵 압축 기법에 비해 48\% 빠른 질의 처리 시간을 필요로 함을 확인한다.Chapter 1 Introduction 1 1.1 Contribution 3 1.2 Organization 5 Chapter 2 Background 6 2.1 Model of Computation 6 2.2 Succinct Data Structures 7 Chapter 3 Space-efficient Representation of Integer Arrays 9 3.1 Introduction 9 3.2 Preliminaries 10 3.2.1 Universal Code System 10 3.2.2 Bit Vector 13 3.3 Algorithm Description 13 3.3.1 Main Principle 14 3.3.2 Optimization in the Implementation 16 3.4 Experimental Results 16 Chapter 4 Space-efficient Parallel Compressed Bitmap Index Processing 19 4.1 Introduction 19 4.2 Related Work 23 4.2.1 Byte-aligned Bitmap Code (BBC) 24 4.2.2 Word-Aligned Hybrid (WAH) 27 4.2.3 WAH-derived Algorithms 28 4.2.4 GPU-based WAH Algorithms 31 4.2.5 Super Byte-aligned Hybrid (SBH) 33 4.3 Parallelizing SBH 38 4.3.1 CPU Parallelism 38 4.3.2 GPU Parallelism 39 4.4 Experimental Results 40 4.4.1 Plain Version 41 4.4.2 Parallelized Version 46 4.4.3 Summary 49 Chapter 5 Space-efficient Representation of Semi-structured Document Formats 50 5.1 Preliminaries 50 5.1.1 Semi-structured Document Formats 50 5.1.2 Resource Description Framework 57 5.1.3 Succinct Ordinal Tree Representations 60 5.1.4 String Compression Schemes 64 5.2 Representation 66 5.2.1 Bit String Indexed Array 67 5.2.2 Main Structure 68 5.2.3 Single Document as a Collection of Chunks 72 5.2.4 Supporting Queries 73 5.3 Experimental Results 75 5.3.1 Datasets 76 5.3.2 Construction Time 78 5.3.3 RAM Usage during Construction 80 5.3.4 Disk Usage and Serialization Time 83 5.3.5 Chunk Division 83 5.3.6 String Compression 88 5.3.7 Query Time 89 Chapter 6 Conclusion 94 Bibliography 96 요약 109 Acknowledgements 111Docto

Fast and Tiny Structural Self-Indexes for XML

XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. Here a fully-fledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slow-down that is comparable to the space improvement. More interestingly, certain algorithms execute much faster over the index (because no decompression occurs). E.g., for structural XPath count queries, evaluating over the index is faster than previous XPath implementations, often by two orders of magnitude. The index also allows to serialize XML results (including texts) faster than previous systems, by a factor of ca. 2-3. This is due to efficient copy handling of grammar repetitions, and because materialization is totally avoided. In order to compare with twig join implementations, we implemented a materializer which writes out pre-order numbers of result nodes, and show its competitiveness.Comment: 13 page

TERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM data

High-throughput data collection in crystallography poses significant challenges in handling massive amounts of data. Here, TERSE/PROLIX (or TRPX for short) is presented, a novel lossless compression algorithm specifically designed for diffraction data. The algorithm is compared with established lossless compression algorithms implemented in gzip, bzip2, CBF (crystallographic binary file), Zstandard(zstd), LZ4 and HDF5 with gzip, LZF and bitshuffle+LZ4 filters, in terms of compression efficiency and speed, using continuous-rotation electron diffraction data of an inorganic compound and raw cryo-EM data. The results show that TRPX significantly outperforms all these algorithms in terms of speed and compression rate. It was 60 times faster than bzip2 (which achieved a similar compression rate), and more than 3 times faster than LZ4, which was the runner-up in terms of speed, but had a much worse compression rate. TRPX files are byte-order independent and upon compilation the algorithm occupies very little memory. It can therefore be readily implemented in hardware. By providing a tailored solution for diffraction and raw cryo-EM data, TRPX facilitates more efficient data analysis and interpretation while mitigating storage and transmission concerns. The C++20 compression/decompression code, custom TIFF library and an ImageJ/Fiji Java plugin for reading TRPX files are open-sourced on GitHub under the permissive MIT license

Secure and efficient storage of multimedia: content in public cloud environments using joint compression and encryption

The Cloud Computing is a paradigm still with many unexplored areas ranging from the technological component to the de nition of new business models, but that is revolutionizing the way we design, implement and manage the entire infrastructure of information technology. The Infrastructure as a Service is the delivery of computing infrastructure, typically a virtual data center, along with a set of APIs that allow applications, in an automatic way, can control the resources they wish to use. The choice of the service provider and how it applies to their business model may lead to higher or lower cost in the operation and maintenance of applications near the suppliers. In this sense, this work proposed to carry out a literature review on the topic of Cloud Computing, secure storage and transmission of multimedia content, using lossless compression, in public cloud environments, and implement this system by building an application that manages data in public cloud environments (dropbox and meocloud). An application was built during this dissertation that meets the objectives set. This system provides the user a wide range of functions of data management in public cloud environments, for that the user only have to login to the system with his/her credentials, after performing the login, through the Oauth 1.0 protocol (authorization protocol) is generated an access token, this token is generated only with the consent of the user and allows the application to get access to data/user les without having to use credentials. With this token the framework can now operate and unlock the full potential of its functions. With this application is also available to the user functions of compression and encryption so that user can make the most of his/her cloud storage system securely. The compression function works using the compression algorithm LZMA being only necessary for the user to choose the les to be compressed. Relatively to encryption it will be used the encryption algorithm AES (Advanced Encryption Standard) that works with a 128 bit symmetric key de ned by user. We build the research into two distinct and complementary parts: The rst part consists of the theoretical foundation and the second part is the development of computer application where the data is managed, compressed, stored, transmitted in various environments of cloud computing. The theoretical framework is organized into two chapters, chapter 2 - Background on Cloud Storage and chapter 3 - Data compression. Sought through theoretical foundation demonstrate the relevance of the research, convey some of the pertinent theories and input whenever possible, research in the area. The second part of the work was devoted to the development of the application in cloud environment. We showed how we generated the application, presented the features, advantages, and safety standards for the data. Finally, we re ect on the results, according to the theoretical framework made in the rst part and platform development. We think that the work obtained is positive and that ts the goals we set ourselves to achieve. This research has some limitations, we believe that the time for completion was scarce and the implementation of the platform could bene t from the implementation of other features.In future research it would be appropriate to continue the project expanding the capabilities of the application, test the operation with other users and make comparative tests.A Computação em nuvem é um paradigma ainda com muitas áreas por explorar que vão desde a componente tecnológica à definição de novos modelos de negócio, mas que está a revolucionar a forma como projetamos, implementamos e gerimos toda a infraestrutura da tecnologia da informação. A Infraestrutura como Serviço representa a disponibilização da infraestrutura computacional, tipicamente um datacenter virtual, juntamente com um conjunto de APls que permitirá que aplicações, de forma automática, possam controlar os recursos que pretendem utilizar_ A escolha do fornecedor de serviços e a forma como este aplica o seu modelo de negócio poderão determinar um maior ou menor custo na operacionalização e manutenção das aplicações junto dos fornecedores. Neste sentido, esta dissertação propôs· se efetuar uma revisão bibliográfica sobre a temática da Computação em nuvem, a transmissão e o armazenamento seguro de conteúdos multimédia, utilizando a compressão sem perdas, em ambientes em nuvem públicos, e implementar um sistema deste tipo através da construção de uma aplicação que faz a gestão dos dados em ambientes de nuvem pública (dropbox e meocloud). Foi construída uma aplicação no decorrer desta dissertação que vai de encontro aos objectivos definidos. Este sistema fornece ao utilizador uma variada gama de funções de gestão de dados em ambientes de nuvem pública, para isso o utilizador tem apenas que realizar o login no sistema com as suas credenciais, após a realização de login, através do protocolo Oauth 1.0 (protocolo de autorização) é gerado um token de acesso, este token só é gerado com o consentimento do utilizador e permite que a aplicação tenha acesso aos dados / ficheiros do utilizador ~em que seja necessário utilizar as credenciais. Com este token a aplicação pode agora operar e disponibilizar todo o potencial das suas funções. Com esta aplicação é também disponibilizado ao utilizador funções de compressão e encriptação de modo a que possa usufruir ao máximo do seu sistema de armazenamento cloud com segurança. A função de compressão funciona utilizando o algoritmo de compressão LZMA sendo apenas necessário que o utilizador escolha os ficheiros a comprimir. Relativamente à cifragem utilizamos o algoritmo AES (Advanced Encryption Standard) que funciona com uma chave simétrica de 128bits definida pelo utilizador. Alicerçámos a investigação em duas partes distintas e complementares: a primeira parte é composta pela fundamentação teórica e a segunda parte consiste no desenvolvimento da aplicação informática em que os dados são geridos, comprimidos, armazenados, transmitidos em vários ambientes de computação em nuvem. A fundamentação teórica encontra-se organizada em dois capítulos, o capítulo 2 - "Background on Cloud Storage" e o capítulo 3 "Data Compression", Procurámos, através da fundamentação teórica, demonstrar a pertinência da investigação. transmitir algumas das teorias pertinentes e introduzir, sempre que possível, investigações existentes na área. A segunda parte do trabalho foi dedicada ao desenvolvimento da aplicação em ambiente "cloud". Evidenciámos o modo como gerámos a aplicação, apresentámos as funcionalidades, as vantagens. Por fim, refletimos sobre os resultados , de acordo com o enquadramento teórico efetuado na primeira parte e o desenvolvimento da plataforma. Pensamos que o trabalho obtido é positivo e que se enquadra nos objetivos que nos propusemos atingir. Este trabalho de investigação apresenta algumas limitações, consideramos que o tempo para a sua execução foi escasso e a implementação da plataforma poderia beneficiar com a implementação de outras funcionalidades. Em investigações futuras seria pertinente dar continuidade ao projeto ampliando as potencialidades da aplicação, testar o funcionamento com outros utilizadores e efetuar testes comparativos.Fundação para a Ciência e a Tecnologia (FCT

Content-aware partial compression for textual big data analysis in Hadoop

A substantial amount of information in companies and on the Internet is present in the form of text. The value of this semi-structured and unstructured data has been widely acknowledged, with consequent scientific and commercial exploitation. The ever-increasing data production, however, pushes data analytic platforms to their limit. Compression as an effective means to reduce data size has been employed by many emerging data analytic platforms, whom the main purpose of data compression is to save storage space and reduce data transmission cost over the network. Since general purpose compression methods endeavour to achieve higher compression ratios by leveraging data transformation techniques and contextual data, this context-dependency forces the access to the compressed data to be sequential. Processing such compressed data in parallel, such as desirable in a distributed environment, is extremely challenging. This work proposes techniques for more efficient textual big data analysis with an emphasis on content-aware compression schemes suitable for the Hadoop analytic platform. The compression schemes have been evaluated for a number of standard MapReduce analysis tasks using a collection of public and private real-world datasets. In comparison with existing solutions, they have shown substantial improvement in performance and significant reduction in system resource requirements

The Family of MapReduce and Large Scale Data Processing Systems

In the last two decades, the continuous increase of computational power has produced an overwhelming flow of data which has called for a paradigm shift in the computing architecture and large scale data processing mechanisms. MapReduce is a simple and powerful programming model that enables easy development of scalable parallel applications to process vast amounts of data on large clusters of commodity machines. It isolates the application from the details of running a distributed program such as issues on data distribution, scheduling and fault tolerance. However, the original implementation of the MapReduce framework had some limitations that have been tackled by many research efforts in several followup works after its introduction. This article provides a comprehensive survey for a family of approaches and mechanisms of large scale data processing mechanisms that have been implemented based on the original idea of the MapReduce framework and are currently gaining a lot of momentum in both research and industrial communities. We also cover a set of introduced systems that have been implemented to provide declarative programming interfaces on top of the MapReduce framework. In addition, we review several large scale data processing systems that resemble some of the ideas of the MapReduce framework for different purposes and application scenarios. Finally, we discuss some of the future research directions for implementing the next generation of MapReduce-like solutions.Comment: arXiv admin note: text overlap with arXiv:1105.4252 by other author

Rapidgzip: Parallel Decompression and Seeking in Gzip Files Using Cache Prefetching

Gzip is a file compression format, which is ubiquitously used. Although a multitude of gzip implementations exist, only pugz can fully utilize current multi-core processor architectures for decompression. Yet, pugz cannot decompress arbitrary gzip files. It requires the decompressed stream to only contain byte values 9-126. In this work, we present a generalization of the parallelization scheme used by pugz that can be reliably applied to arbitrary gzip-compressed data without compromising performance. We show that the requirements on the file contents posed by pugz can be dropped by implementing an architecture based on a cache and a parallelized prefetcher. This architecture can safely handle faulty decompression results, which can appear when threads start decompressing in the middle of a gzip file by using trial and error. Using 128 cores, our implementation reaches 8.7 GB/s decompression bandwidth for gzip-compressed base64-encoded data, a speedup of 55 over the single-threaded GNU gzip, and 5.6 GB/s for the Silesia corpus, a speedup of 33 over GNU gzip.Comment: HPDC'2