Improved Compressed String Dictionaries

In a 2-dimensional (2D) pattern matching problem, the text is arranged as a matrix 𝖬[1..n, 1..n] and consists of N = n × n symbols drawn from alphabet set Σ of size σ. The query consists of a m × m square matrix 𝖯[1..m, 1..m] drawn from the same alphabet set Σ and the task is to find all the locations in 𝖬 where 𝖯 appears as a (contiguous) submatrix. The patterns can be of any size, but as long as they are square in shape data structures like suffix trees and suffix array exist [Raffaele Giancarlo, 1995; Dong Kyue Kim et al., 1998] for the task of efficient pattern matching. These are essentially 2D counterparts of classic suffix trees and arrays known for traditional 1-dimensional (1D) pattern matching. They work based on linearization of 2D suffixes which would preserve the prefix match property (i.e., every pattern match is a prefix of some suffix). The main limitation of the suffix trees and the suffix arrays (in 1D) was their space utilization of O(N log N) bits, where N is the size of the text. This was suboptimal compared to Nlog σ bits of space, which is information theoretic optimal for the text. With the advent of the field of succinct/compressed data structures, it was possible to develop compressed variants of suffix trees and array based on Burrows-Wheeler Tansform and LF-mapping (or Φ function) [Roberto Grossi and Jeffrey Scott Vitter, 2005; Paolo Ferragina and Giovanni Manzini, 2005; Kunihiko Sadakane, 2007]. These data structures indeed achieve O(N log σ) bits of space or better. This gives rise to the question: analogous to 1D case, can we design a succinct or compressed index for 2D pattern matching? Can there be a 2D compressed suffix tree? Are there analogues of Burrows-Wheeler Transform or LF-mapping? The problem has been acknowledged for over a decade now and there have been a few attempts at applying Φ function [Ankur Gupta, 2004] and achieving entropy based compression [Veli Mäkinen and Gonzalo Navarro, 2008]. However, achieving the complexity breakthrough akin to 1D case has yet to be found. In this paper, we still do not know how to answer suffix array queries in O(N log σ) bits of space - which would have led to efficient pattern matching. However, for the first time, we show an interesting result that it is indeed possible to compute inverse suffix array (ISA) queries in near compact space in O(polylog n) time. Our 2D succinct text index design is based on two 1D compressed suffix trees and it takes O(N log log N + N logσ) bits of space which is much smaller than its naive design that takes O(N log N) bits. Although the main problem is still evasive, this index gives a hope on the existence of a full 2D succinct index with all functionalities similar to that of 1D case.

The suffix array $SA[1..n]$ of a text $T$ of length $n$ is a permutation of $\{1,\ldots,n\}$ describing the lexicographical ordering of suffixes of $T$, and it is considered to be among of the most important data structures in string algorithms, with dozens of applications in data compression, bioinformatics, and information retrieval. One of the biggest drawbacks of the suffix array is that it is very difficult to maintain under text updates: even a single character substitution can completely change the contents of the suffix array. Thus, the suffix array of a dynamic text is modelled using suffix array queries, which return the value $SA[i]$ given any $i\in[1..n]$. Prior to this work, the fastest dynamic suffix array implementations were by Amir and Boneh. At ISAAC 2020, they showed how to answer suffix array queries in $\tilde{O}(k)$ time, where $k\in[1..n]$ is a trade-off parameter, with $\tilde{O}(\frac{n}{k})$-time text updates. In a very recent preprint [2021], they also provided a solution with $O(\log^5 n)$-time queries and $\tilde{O}(n^{2/3})$-time updates. We propose the first data structure that supports both suffix array queries and text updates in $O({\rm polylog}\,n)$ time (achieving $O(\log^4 n)$ and $O(\log^{3+o(1)} n)$ time, respectively). Our data structure is deterministic and the running times for all operations are worst-case. In addition to the standard single-character edits (character insertions, deletions, and substitutions), we support (also in $O(\log^{3+o(1)} n)$ time) the "cut-paste" operation that moves any (arbitrarily long) substring of $T$ to any place in $T$. We complement our structure by a hardness result: unless the Online Matrix-Vector Multiplication (OMv) Conjecture fails, no data structure with $O({\rm polylog}\,n)$-time suffix array queries can support the "copy-paste" operation in $O(n^{1-\epsilon})$ time for any $\epsilon>0$.

String dictionaries constitute a large portion of the memory footprint of database applications. While strong string dictionary compression algorithms exist, these come with impractical access and compression times. Therefore, lightweight algorithms such as front coding (PFC) are favored in practice. This paper endeavors to make strong string dictionary compression practical. We focus on Re-Pair Front Coding (RPFC), a grammar-based compression algorithm, since it consistently offers better compression ratios than other algorithms in the literature. To accelerate compression times, we propose block-based RPFC (BRPFC) which consists in independently compressing small blocks of the dictionary. For further accelerated compression times especially on large string dictionaries, we also propose an alternative version of BRPFC that uses sampling to speed up compression. Moreover, to accelerate access times, we devise a vectorized access method, using hbox {Intel}^{circledR } Advanced Vector Extensions 512 (hbox {Intel}^{circledR } AVX-512). Our experimental evaluation shows that sampled BRPFC offers compression times up to 190 times faster than RPFC, and random string lookups 2.3 times faster than RPFC on average. These results move our modified RPFC into a practical range for use in database systems because the overhead of Re-Pair-based compression for access times can be reduced by 2 times .

Byte addressable non-volatile (NV) memory, such as STT-RAM, MRAM, and PCM, is the next generation memory that can be used as both main memory and secondary storage. While it can persistently store data without power supply, its access speed is comparable to DRAM. While there have been the active researches on its use for either main memory or secondary storage, these researches were conducted independently. This paper presents the integration methods of the main memory and file system management for NV memory, so that it can be used as both main memory and storage. The presented methods use a file system as their basis for the NV memory management; thus, the internal data structures of a file system can have impacts upon the performance of the integration methods. We implemented the proposed methods in the Linux kernel, and performed the evaluation on a system emulator. The evaluation results show that 1) the proposed methods can perform comparably to the existing DRAM memory allocator and significantly better than the page swapping, 2) their performance is affected by the internal data structures of a file system, and 3) the data structures appropriate for traditional hard disk drives do not always work effectively for byte addressable NV memory.

This paper gives an introduction to Web mining, then describes Web Structure mining in detail, and explores the data structure used by the Web. This paper also explores different Page Rank algorithms and compare those algorithms used for Information Retrieval. In Web Mining, the basics of Web mining and the Web mining categories are explained. Different Page Rank based algorithms like PageRank (PR), WPR (Weighted PageRank), HITS (Hyperlink-Induced Topic Search), DistanceRank and DirichletRank algorithms are discussed and compared. PageRanks are calculated for PageRank and Weighted PageRank algorithms for a given hyperlink structure. Simulation Program is developed for PageRank algorithm because PageRank is the only ranking algorithm implemented in the search engine (Google). The outputs are shown in a table and chart format.

We introduce a new text-indexing data structure, the String B-Tree , that can be seen as a link between some traditional external-memory and string-matching data structures. In a short phrase, it is a combination of B-trees and Patricia tries for internal-node indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String B-Tree overcomes the theoretical limitations of inverted files, B-trees, prefix B-trees, suffix arrays, compacted tries and suffix trees. String B-trees have the same worst-case performance as B-trees but they manage unbounded-length strings and perform much more powerful search operations such as the ones supported by suffix trees. String B-trees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication.

Suffix Array (SA) is a data structure formed by sorting the suffixes of a string into lexicographic order. SAs have been used in a variety of applications, most notably in pattern matching and Burrows-Wheeler Transform (BWT) based lossless data compression. SAs have also become the data structure of choice for many, if not all, string processing problems to which suffix tree methodology is applicable. Over the last two decades researchers have proposed many suffix array construction algorithm (SACAs). We do a systematic study of the main classes of SACAs with the intent of mapping them onto a data parallel architecture like the GPU. We conclude that skew algorithm [12], a linear time recursive algorithm, is the best candidate for GPUs as all its phases can be efficiently mapped to a data parallel hardware. Our OpenCL implementation of skew algorithm achieves a throughput of up to 25 MStrings/sec and a speedup of up to 34x and 5.8x over a single threaded CPU implementation using a discrete GPU and APU respectively. We also compare our OpenCL implementation against the fastest known CPU implementation based on induced copying and achieve a speedup of up to 3.7x. Using SA we construct BWT on GPU and achieve a speedup of 11x over the fastest known BWT on GPU.

String matching is a ubiquitous problem that arises in a wide range of applications in computing, e.g., packet routing, intrusion detection, web querying, and genome analysis. Due to its importance, dozens of algorithms and several data structures have been developed over the years. A recent breakthrough in this field is the FM-index, a data structure that synergistically combines the Burrows-Wheeler transform and the suffix array. In software, the FM-index allows searching (exact and approximate) in times comparable to the fastest known indices for large texts (suffix trees and suffix arrays), but has the additional advantage of being more space-efficient than those approaches. In this paper, we describe the first FPGA-based hardware implementation of the FM-index for exact pattern matching. We report experimental results on the problem of mapping short DNA sequences to a reference genome. We show that the throughput of the FM-index is significantly higher than the naive (brute force) approach. Like the Bowtie software tool, the FM-index can abandon early the hardware matching. It outperforms Bowtie by two orders of magnitude.

The field of stringology studies algorithms and data structures used for processing strings efficiently. The goal of this thesis is to investigate 2-dimensional (2D) variants of some fundamental string problems, including \textit{Exact Pattern Matching} and \textit{Longest Common Substring}. In the 2D pattern matching problem, we are given a matrix $\M[1\dd n,1\dd n]$ that consists of $N = n \times n$ symbols drawn from an alphabet $\Sigma$ of size $\sigma$. The query consists of a $ m \times m$ square matrix $\PP[1\dd m, 1\dd m]$ drawn from the same alphabet, and the task is to find all the locations of $\PP$ in $\M$. For such square patterns, data structures such as suffix trees and suffix arrays exist for the task of efficient pattern matching. However, a suffix tree occupies $O(N \log N)$ bits, which is significantly more than that of the original text's size of $N\log \sigma$ bits. Therefore, the design of compressed data structures, that supports pattern matching queries efficiently and occupies space close to the original text's size, is imperative. In this thesis, we show an interesting result by designing a compact text index of size $O(N \log\log N + N \log\sigma)$ bits that at least supports efficient inverse suffix array queries. Although, the question of designing a compressed text index that would lead to efficient pattern matching is still evasive, this index gives a hope on the existence of a full 2D compressed text index with all functionalities similar to that of 1D case. On the other hand, the Longest Common 2D substring problem consists of two 2D strings (matrices), and the task is to report the size of the longest common 2D substring (submatrix) of these 2D strings. It is interesting to know if there exists a sublinear-time algorithm for solving this task. We answer this question positively by presenting a sublinear-time \textit{quantum} algorithm. In addition to this, we prove that any quantum algorithm requires at least $\tilde{\Omega}(N^{2/3})$ time to solve this problem.

MotivationIndexing reference sequences for search—both individual genomes and collections of genomes—is an important building block for many sequence analysis tasks. Much work has been dedicated to developing full-text indices for genomic sequences, based on data structures such as the suffix array, the BWT and the FM-index. However, the de Bruijn graph, commonly used for sequence assembly, has recently been gaining attention as an indexing data structure, due to its natural ability to represent multiple references using a graphical structure, and to collapse highly-repetitive sequence regions. Yet, much less attention has been given as to how to best index such a structure, such that queries can be performed efficiently and memory usage remains practical as the size and number of reference sequences being indexed grows large.ResultsWe present a novel data structure for representing and indexing the compacted colored de Bruijn graph, which allows for efficient pattern matching and retrieval of the reference information associated with each k-mer. As the popularity of the de Bruijn graph as an index has increased over the past few years, so have the number of proposed representations of this structure. Existing structures typically fall into two categories; those that are hashing-based and provide very fast access to the underlying k-mer information, and those that are space-frugal and provide asymptotically efficient but practically slower pattern search. Our representation achieves a compromise between these two extremes. By building upon minimum perfect hashing and making use of succinct representations where applicable, our data structure provides practically fast lookup while greatly reducing the space compared to traditional hashing-based implementations. Further, we describe a sampling scheme for this index, which provides the ability to trade off query speed for a reduction in the index size. We believe this representation strikes a desirable balance between speed and space usage, and allows for fast search on large reference sequences.Finally, we describe an application of this index to the taxonomic read assignment problem. We show that by adopting, essentially, the approach of Kraken, but replacing k-mer presence with coverage by chains of consistent unique maximal matches, we can improve the space, speed and accuracy of taxonomic read assignment.Availability and implementationpufferfish is written in C++11, is open source, and is available at https://github.com/COMBINE-lab/pufferfish.Supplementary informationSupplementary data are available at Bioinformatics online.

Given a set D={d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,..., d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> } of D strings of total length n, our task is to report the "most relevant"strings for a given query pattern P. This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of "most relevant" is involved. In information retrieval literature, this task is best achieved by using inverted indexes. However, inverted indexes work only for some predefined set of patterns. In the pattern matching community, the most popular pattern-matching data structures are suffix trees and suffix arrays. However, a typical suffix tree search involves going through all the occurrences of the pattern over the entire string collection, which might be a lot more than the required relevant documents. The first formal framework to study such kind of retrieval problems was given by Muthukrishnan. He considered two metrics for relevance: frequency and proximity. He took a threshold-based approach on these metrics and gave data structures taking O(n log n) words of space. We study this problem in a slightly different framework of reporting the top k most relevant documents (in sorted order) under similar and more general relevance metrics. Our framework gives linear space data structure with optimal query times for arbitrary score functions. As a corollary, it improves the space utilization for the problems in while maintaining optimal query performance. We also develop compressed variants of these data structures for several specific relevance metrics.

We introduce a new data structure, a localized suffix array, based on which occurrence information is dynamically represented as the combination of global positional information and local lexicographic order information in text search applications. For the search of a pair of words within a given distance, many candidate positions that share a coarse-grained global position can be compactly represented in term of local lexicographic orders as in the conventional suffix array, and they can be simultaneously examined for violation of the distance constraint at the coarse-grained resolution. Trade-off between the positional and lexicographical information is progressively shifted towards finer positional resolution, and the distance constraint is reexamined accordingly. Thus the paired search can be efficiently performed even if there are a large number of occurrences for each word. The localized suffix array itself is in fact a reordering of bits inside the conventional suffix array, and their memory requirements are essentially the same. We demonstrate an application to genome mapping problems for paired-end short reads generated by new-generation DNA sequencers. When paired reads are highly repetitive,

Interactive out-of-core isosurface visualisation in time-varying data sets

Sequences occur naturally in many domains such as biology, engineering, finance and scientific research. Since humans have the inherent ability to comprehend and utilize sequences in day to day cognitive tasks such as speech, vision and motor control; biologically inspired sequence learning techniques are used for explanatory data analysis in these domains. Identifying the common substrings which exist in sequences helps in determining the underlying structure and calculating the similarity between sequences. The suffix trie, suffix tree and suffix array are data structures which are used in many solutions to sequence based problems. However, these are static data structures and not flexible tools which can be used for sequence learning. In this paper we present the Adaptive Suffix Trie algorithm, a sequence learning algorithm which can be used for identifying substrings of different lengths and frequencies from a given set of sequences. In contrast to suffix data structures which store all suffixes, the adaptive suffix trie only captures the frequent substrings that occur in the given dataset, resulting in a less complex structure with only the relevant or useful information. We show how the algorithms' learning parameters can be adapted for extracting substrings with the required characteristics and then demonstrate it's application in the classification of biological sequences.

With the rapid growth of the Web data, for the phenomenon of data explosion but poor knowledge, as the data mining based on database table has been unable to meet the needs of Web application, a distributed Web mining is becoming a research hot spot presently. Firstly, based on the research of web mining, XML is used to transform semi-structured data to well structured data, and a distributed web mining model based on XML is deeply discussed. Then, a mobile agent technology is introduced into the design of Web mining system, and a distributed Web mining structure based on data mining agent is built. Finally, an architecture design of network teaching platform based on XML and agents is realized, which can provide intelligent aids for personalized learning, thus greatly improve the teaching efficiency of network teaching platform.