348 research outputs found
Lempel-Ziv Parsing in External Memory
For decades, computing the LZ factorization (or LZ77 parsing) of a string has
been a requisite and computationally intensive step in many diverse
applications, including text indexing and data compression. Many algorithms for
LZ77 parsing have been discovered over the years; however, despite the
increasing need to apply LZ77 to massive data sets, no algorithm to date scales
to inputs that exceed the size of internal memory. In this paper we describe
the first algorithm for computing the LZ77 parsing in external memory. Our
algorithm is fast in practice and will allow the next generation of text
indexes to be realised for massive strings and string collections.Comment: 10 page
The Rightmost Equal-Cost Position Problem
LZ77-based compression schemes compress the input text by replacing factors
in the text with an encoded reference to a previous occurrence formed by the
couple (length, offset). For a given factor, the smallest is the offset, the
smallest is the resulting compression ratio. This is optimally achieved by
using the rightmost occurrence of a factor in the previous text. Given a cost
function, for instance the minimum number of bits used to represent an integer,
we define the Rightmost Equal-Cost Position (REP) problem as the problem of
finding one of the occurrences of a factor which cost is equal to the cost of
the rightmost one. We present the Multi-Layer Suffix Tree data structure that,
for a text of length n, at any time i, it provides REP(LPF) in constant time,
where LPF is the longest previous factor, i.e. the greedy phrase, a reference
to the list of REP({set of prefixes of LPF}) in constant time and REP(p) in
time O(|p| log log n) for any given pattern p
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
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
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
Fast online Lempel-Ziv factorization in compressed space
Let T be a text of length n on an alphabet \u3a3 of size \u3c3, and let H0 be the zero-order empirical entropy of T. We show that the LZ77 factorization of T can be computed in nH0+o(nlog\u3c3)+O(\u3c3logn) bits of working space with an online algorithm running in O(nlogn) time. Previous space-efficient online solutions either work in compact space and O(nlogn) time, or in succinct space and O(nlog3n) time
A new word-based compression model allowing compressed pattern matching
In this study a new semistatic data compression model that has a fast coding process and that allows compressed pattern matching is introduced. The name of the proposed model is chosen as tagged word-based compression algorithm (TWBCA) since it has a word-based coding and word-based compressed matching algorithm. The model has two phases. In the first phase a dictionary is constructed by adding a phrase, paying attention to word boundaries, and in the second phase compression is done by using codewords of phrases in this dictionary. The first byte of the codeword determines whether the word is compressed or not. By paying attention to this rule, the CPM process can be conducted as word based. In addition, the proposed method makes it possible to also search for the group of consecutively compressed words. Any of the previous pattern matching algorithms can be chosen to use in compressed pattern matching as a black box. The duration of the CPM process is always less than the duration of the same process on the texts coded by Gzip tool. While matching longer patterns, compressed pattern matching takes more time on the texts coded by compress and end-tagged dense code (ETDC). However, searching shorter patterns takes less time on texts coded by our approach than the texts compressed with compress. Besides this, the compression ratio of our algorithm has a better performance against ETDC only on a file that has been written in Turkish. The compression performance of TWBCA is stable and does not vary over 6% on different text files
Bicriteria data compression
The advent of massive datasets (and the consequent design of high-performing
distributed storage systems) have reignited the interest of the scientific and
engineering community towards the design of lossless data compressors which
achieve effective compression ratio and very efficient decompression speed.
Lempel-Ziv's LZ77 algorithm is the de facto choice in this scenario because of
its decompression speed and its flexibility in trading decompression speed
versus compressed-space efficiency. Each of the existing implementations offers
a trade-off between space occupancy and decompression speed, so software
engineers have to content themselves by picking the one which comes closer to
the requirements of the application in their hands. Starting from these
premises, and for the first time in the literature, we address in this paper
the problem of trading optimally, and in a principled way, the consumption of
these two resources by introducing the Bicriteria LZ77-Parsing problem, which
formalizes in a principled way what data-compressors have traditionally
approached by means of heuristics. The goal is to determine an LZ77 parsing
which minimizes the space occupancy in bits of the compressed file, provided
that the decompression time is bounded by a fixed amount (or vice-versa). This
way, the software engineer can set its space (or time) requirements and then
derive the LZ77 parsing which optimizes the decompression speed (or the space
occupancy, respectively). We solve this problem efficiently in O(n log^2 n)
time and optimal linear space within a small, additive approximation, by
proving and deploying some specific structural properties of the weighted graph
derived from the possible LZ77-parsings of the input file. The preliminary set
of experiments shows that our novel proposal dominates all the highly
engineered competitors, hence offering a win-win situation in theory&practice
Enhancing Text Compression Method Using Information Source Indexing
Text compression methods where the original texts are directly mapped into binary domain are attractive to compress English text files. This paper proposes an intermediate mapping scheme in which the original English text is transformed firstly to decimal domain and then to binary domain. Each two-decimal-digit value in the resulting intermediate decimal file represents the index to the location of each alphabet found in the original text. If the already indexed alphabet is seen again, it will be replaced by the previously given decimal-index number. The decimal file is converted into binary domain by assigning each decimal digit a 4-bit weighted code in according to its frequency of occurrence that is akin to BCD code. The assigned codes aim at generating an equivalent binary file with entropy as close as much to that of the original one. Thereafter, any conventional compression algorithm such as Lempel-Ziv algorithms can be applied to the generated binary file. The obtained compression ratios outperform those ones obtained when applying the same compression algorithm to the binary files generated either via direct mapping of the original text or via mapping the decimal file using Binary Coded Decimal (BCD) codes. Keywords: Lossless data compression; Source encoding, LZW coding, Hamming weights, Compression ratio
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