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BZIP
bzip2 is a free and open-source file compression program that uses the Burrows–Wheeler algorithm. It only compresses single files and is not a file archiver. It relies on separate external utilities such as tar for tasks such as handling multiple files, and other tools for encryption, and archive splitting. bzip2 was initially released in 1996 by Julian Seward. It compresses most files more effectively than older LZW and Deflate compression algorithms but is slower. bzip2 is particularly efficient for text data, and decompression is relatively fast. The algorithm uses several layers of compression techniques, such as run-length encoding (RLE), Burrows–Wheeler transform (BWT), move-to-front transform (MTF), and Huffman coding. bzip2 compresses data in blocks between 100 and 900 kB and uses the Burrows–Wheeler transform to convert frequently recurring character sequences into strings of identical letters. The move-to-front transform and Huffman coding are then a ...
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Multithreading (software)
In computer science, a thread of execution is the smallest sequence of programmed instructions that can be managed independently by a scheduler, which is typically a part of the operating system. In many cases, a thread is a component of a process. The multiple threads of a given process may be executed concurrently (via multithreading capabilities), sharing resources such as memory, while different processes do not share these resources. In particular, the threads of a process share its executable code and the values of its dynamically allocated variables and non- thread-local global variables at any given time. The implementation of threads and processes differs between operating systems. History Threads made an early appearance under the name of "tasks" in IBM's batch processing operating system, OS/360, in 1967. It provided users with three available configurations of the OS/360 control system, of which Multiprogramming with a Variable Number of Tasks (MVT) was ...
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Canonical Huffman Code
In computer science and information theory, a canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described in a very compact manner. Rather than storing the structure of the code tree explicitly, canonical Huffman codes are ordered in such a way that it suffices to only store the lengths of the codewords, which reduces the overhead of the codebook. Motivation Data compressors generally work in one of two ways. Either the decompressor can infer what codebook the compressor has used from previous context, or the compressor must tell the decompressor what the codebook is. Since a canonical Huffman codebook can be stored especially efficiently, most compressors start by generating a "normal" Huffman codebook, and then convert it to canonical Huffman before using it. In order for a symbol code scheme such as the Huffman code to be decompressed, the same model that the encoding algorithm used to compress the source data must be ...
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Move-to-front Transform
The move-to-front (MTF) transform is an encoding of data (typically a stream of bytes) designed to improve the performance of entropy encoding techniques of compression. When efficiently implemented, it is fast enough that its benefits usually justify including it as an extra step in data compression algorithm. This algorithm was first published by Boris Ryabko under the name of "book stack" in 1980. Subsequently, it was rediscovered by J.K. Bentley et al. in 1986, as attested in the explanatory note. The transform The main idea is that each symbol in the data is replaced by its index in the stack of “recently used symbols”. For example, long sequences of identical symbols are replaced by as many zeroes, whereas when a symbol that has not been used in a long time appears, it is replaced with a large number. Thus at the end the data is transformed into a sequence of integers; if the data exhibits a lot of local correlations, then these integers tend to be small. Let us gi ...
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Bijective Numeration
Bijective numeration is any numeral system in which every non-negative integer can be represented in exactly one way using a finite string of digits. The name refers to the bijection (i.e. one-to-one correspondence) that exists in this case between the set of non-negative integers and the set of finite strings using a finite set of symbols (the "digits"). Most ordinary numeral systems, such as the common decimal system, are not bijective because more than one string of digits can represent the same positive integer. In particular, adding leading zeroes does not change the value represented, so "1", "01" and "001" all represent the number one. Even though only the first is usual, the fact that the others are possible means that the decimal system is not bijective. However, the unary numeral system, with only one digit, ''is'' bijective. A bijective base-''k'' numeration is a bijective positional notation. It uses a string of digits from the set (where ''k'' ≥ 1) to encode ea ...
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Bit Array
A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores ''kw'' bits, where ''w'' is the number of bits in the unit of storage, such as a byte or Word (computer architecture), word, and ''k'' is some nonnegative integer. If ''w'' does not divide the number of bits to be stored, some space is wasted due to Fragmentation (computing), internal fragmentation. Definition A bit array is a mapping from some domain (almost always a range of integers) to values in the set . The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed ...
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Elias Delta Coding
Elias δ code or Elias delta code is a universal code encoding the positive integers developed by Peter Elias. Encoding To code a number ''X'' ≥ 1: # Let ''N'' = ⌊log2 ''X''⌋; be the highest power of 2 in ''X'', so 2''N'' ≤ ''X'' < 2''N''+1. # Let ''L'' = ⌊log2 ''N''+1⌋ be the highest power of 2 in ''N''+1, so 2''L'' ≤ ''N''+1 < 2''L''+1. # Write ''L'' zeros, followed by # the ''L''+1-bit binary representation of ''N''+1, followed by # all but the leading bit (i.e. the last ''N'' bits) of ''X''. An equivalent way to express the same process: #Separate ''X'' into the highest power of 2 it contains (2''N'') and the remaining ''N'' binary digits. #Encode ''N''+1 with Elias gamma coding. #Append the remaining ''N'' binary digits to this representation of ''N''+1. To represent a number x
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Base-1
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number ''N'', a symbol representing 1 is repeated ''N'' times. In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol. Numbers 1, 2, 3, 4, 5, 6, ... are represented in unary as 1, 11, 111, 1111, 11111, 111111, ... Unary is a bijective numeral system. However, although it has sometimes been described as "base 1", it differs in some important ways from positional notations, in which the value of a digit depends on its position within a number. For instance, the unary form of a number can be exponentially longer than its representation in other bases. The use of tally marks in counting is an application of the unary numeral system. For example, using the tally mark (𝍷), the number 3 is represented as . In East Asian cultures, the number 3 is represented as 三, a character drawn with three strokes. (One and two are repres ...
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Move-to-front
The move-to-front (MTF) transform is an encoding of data (typically a stream of bytes) designed to improve the performance of entropy encoding techniques of compression. When efficiently implemented, it is fast enough that its benefits usually justify including it as an extra step in data compression algorithm. This algorithm was first published by Boris Ryabko under the name of "book stack" in 1980. Subsequently, it was rediscovered by J.K. Bentley et al. in 1986, as attested in the explanatory note. The transform The main idea is that each symbol in the data is replaced by its index in the stack of “recently used symbols”. For example, long sequences of identical symbols are replaced by as many zeroes, whereas when a symbol that has not been used in a long time appears, it is replaced with a large number. Thus at the end the data is transformed into a sequence of integers; if the data exhibits a lot of local correlations, then these integers tend to be small. Let us giv ...
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Run-length Encoding
Run-length encoding (RLE) is a form of lossless data compression in which ''runs'' of data (consecutive occurrences of the same data value) are stored as a single occurrence of that data value and a count of its consecutive occurrences, rather than as the original run. As an imaginary example of the concept, when encoding an image built up from colored dots, the sequence "green green green green green green green green green" is shortened to "green x 9". This is most efficient on data that contains many such runs, for example, simple graphic images such as icons, line drawings, games, and animations. For files that do not have many runs, encoding them with RLE could increase the file size. RLE may also refer in particular to an early graphics file format supported by CompuServe for compressing black and white images, that was widely supplanted by their later Graphics Interchange Format (GIF). RLE also refers to a little-used image format in Windows 3.x that is saved with the fil ...
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Apache Spark
Apache Spark is an open-source unified analytics engine for large-scale data processing. Spark provides an interface for programming clusters with implicit data parallelism and fault tolerance. Originally developed at the University of California, Berkeley's AMPLab starting in 2009, in 2013, the Spark codebase was donated to the Apache Software Foundation, which has maintained it since. Overview Apache Spark has its architectural foundation in the resilient distributed dataset (RDD), a read-only multiset of data items distributed over a cluster of machines, that is maintained in a fault-tolerant way. The Dataframe API was released as an abstraction on top of the RDD, followed by the Dataset API. In Spark 1.x, the RDD was the primary application programming interface (API), but as of Spark 2.x use of the Dataset API is encouraged even though the RDD API is not deprecated. The RDD technology still underlies the Dataset API. Spark and its RDDs were developed in 2012 in respon ...
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