Fully Online Grammar Compression in Constant Space

We present novel variants of fully online LCA (FOLCA), a fully online grammar compression that builds a straight line program (SLP) and directly encodes it into a succinct representation in an online manner. FOLCA enables a direct encoding of an SLP into a succinct representation that is asymptotically equivalent to an information theoretic lower bound for representing an SLP (Maruyama et al., SPIRE'13). The compression of FOLCA takes linear time proportional to the length of an input text and its working space depends only on the size of the SLP, which enables us to apply FOLCA to large-scale repetitive texts. Recent repetitive texts, however, include some noise. For example, current sequencing technology has significant error rates, which embeds noise into genome sequences. For such noisy repetitive texts, FOLCA working in the SLP size consumes a large amount of memory. We present two variants of FOLCA working in constant space by leveraging the idea behind stream mining techniques. Experiments using 100 human genomes corresponding to about 300GB from the 1000 human genomes project revealed the applicability of our method to large-scale, noisy repetitive texts.Comment: This is an extended version of a proceeding accepted to Data Compression Conference (DCC), 201

siEDM: an efficient string index and search algorithm for edit distance with moves

Although several self-indexes for highly repetitive text collections exist, developing an index and search algorithm with editing operations remains a challenge. Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string into another. Although the problem of computing EDM is intractable, it has a wide range of potential applications, especially in approximate string retrieval. Despite the importance of computing EDM, there has been no efficient method for indexing and searching large text collections based on the EDM measure. We propose the first algorithm, named string index for edit distance with moves (siEDM), for indexing and searching strings with EDM. The siEDM algorithm builds an index structure by leveraging the idea behind the edit sensitive parsing (ESP), an efficient algorithm enabling approximately computing EDM with guarantees of upper and lower bounds for the exact EDM. siEDM efficiently prunes the space for searching query strings by the proposed method, which enables fast query searches with the same guarantee as ESP. We experimentally tested the ability of siEDM to index and search strings on benchmark datasets, and we showed siEDM's efficiency.Comment: 23 page

Indexing Highly Repetitive String Collections

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 challenges our ability of handling them even in compressed form. It turns out, fortunately, that many of these rapidly growing string collections are highly repetitive, so that their information content is orders of magnitude lower than their plain size. The statistical compression methods used for classical collections, however, are blind to this repetitiveness, and therefore a new set of techniques has been developed in order to properly exploit it. The resulting indexes form a new generation of data structures able to handle the huge repetitive string collections that we are facing. In this survey we cover the algorithmic developments that have led to these data structures. We describe the distinct compression paradigms that have been used to exploit repetitiveness, the fundamental algorithmic ideas that form the base of all the existing indexes, and the various structures that have been proposed, comparing them both in theoretical and practical aspects. We conclude with the current challenges in this fascinating field

Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms

Efficient compression of large repetitive strings

When is comes to managing large volumes of data, general-purpose compressors such as gzip are ubiquitous. They are fast, practical and available on every modern platform from standard desktops to mobile devices. These tools exploit local redundancy in a text using a fixed-size sliding window. This window is usually very small relative to the text, however, in principle it can be as large as available memory. The window acts as a dictionary. Compression is achieved by replacing substrings with pointers to previous occurrences found in the dictionary. This type of algorithm becomes problematic when dealing with collections that are larger than physical memory, as it fails to capture any non-local redundancy, that is, repetition that occurs outside of its search window. With rapid growth in the already enormous amount of data we store and process there is a pressing need for improving compression effectiveness, reducing both storage requirements and decompression costs. However, many systems still use general-purpose compression tools on large highly repetitive data collections. In this thesis we focus on addressing this issue. We explore compression in a variety of domains where large volumes of data need to be stored and accessed, and general-purpose compression tools are cannon. First we discuss our work on web corpus compression, then we discuss the implementation of a practical index for repetitive texts that gives strong theoretical bounds in terms of size and access, and finally, we discuss our work on compression of high-throughput sequencing reads. We show that in all cases, our new methods improve on current techniques in both run-time and compression effectiveness, and provide important functionality such as fast decoding and random access

An Online Algorithm for Lightweight Grammar-Based Compression

Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log2 n)- approximation ratio for the minimum grammar size, where n is an input size, and it runs in input linear time and output linear space. In addition, we propose a practical encoding, which transforms a restricted CFG into a more compact representation. Experimental results by comparison with standard compressors demonstrate that our algorithm is especially effective for highly repetitive text