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In 1968 Shirley Chisholm became the first Black woman elected to the United States Congress. In 1972 she launched a campaign for the Democratic presidential nomination, breaking another political barrier.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In computer science, a compressed suffix array[1][2][3] is a compressed data structure for pattern matching. Compressed suffix arrays are a general class of data structure that improve on the suffix array.[1][2] These data structures enable quick search for an arbitrary string with a comparatively small index.
Given a text T of n characters from an alphabet Σ, a compressed suffix array supports searching for arbitrary patterns in T. For an input pattern P of m characters, the search time is typically O(m) or O(m + log(n)). The space used is typically , where is the k-th order empirical entropy of the text T. The time and space to construct a compressed suffix array are normally .
The original presentation of a compressed suffix array[1] solved a long-standing open problem by showing that fast pattern matching was possible using only a linear-space data structure, namely, one proportional to the size of the text T, which takes bits. The conventional suffix array and suffix tree use bits, which is substantially larger. The basis for the data structure is a recursive decomposition using the "neighbor function," which allows a suffix array to be represented by one of half its length. The construction is repeated multiple times until the resulting suffix array uses a linear number of bits. Following work showed that the actual storage space was related to the -order entropy and that the index supports self-indexing.[4] The space bound was further improved achieving the ultimate goal of higher-order entropy; the compression is obtained by partitioning the neighbor function by high-order contexts, and compressing each partition with a wavelet tree.[3] The space usage is extremely competitive in practice with other state-of-the-art compressors,[5] and it also supports fast in-situ pattern matching.
The memory accesses made by compressed suffix arrays and other compressed data structures for pattern matching are typically not localized, and thus these data structures have been notoriously hard to design efficiently for use in external memory. Recent progress using geometric duality takes advantage of the block access provided by disks to speed up the I/O time significantly[6] In addition, potentially practical search performance for a compressed suffix array in external-memory has been demonstrated.[7]
There are several open source implementations of compressed suffix arrays available (see External links below). Bowtie and Bowtie2 are open-source compressed suffix array implementations of read alignment for use in bioinformatics. The Succinct Data Structure Library (SDSL) is a library containing a variety of compressed data structures including compressed suffix arrays. FEMTO is an implementation of compressed suffix arrays for external memory. In addition, a variety of implementations, including the original FM-index implementations, are available from the Pizza & Chili Website (see external links).
Implementations:
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In computer science, a suffix array is a sorted array of all suffixes of a string. It is a data structure used in, among others, full-text indices, data-compression algorithms, and the field of bibliometrics. Suffix arrays were introduced by Manber & Myers (1990) as a simple, space efficient alternative to suffix trees. They had independently been discovered by Gaston Gonnet in 1987 under the name PAT array (Gonnet, Baeza-Yates & Snider 1992). Li, Li & Huo (2016) gave the first in-place O ( n ) {\displaystyle {\mathcal {O}}(n)} time suffix array construction algorithm that is optimal both in time and space, where in-place means that the algorithm only needs O ( 1 ) {\displaystyle {\mathcal {O}}(1)} additional space beyond the input string and the output suffix array. Enhanced suffix arrays (ESAs) are suffix arrays with additional tables that reproduce the full functionality of suffix trees preserving the same time and memory complexity. A sorted array of only some (rather than all) suffixes of a string is called a sparse suffix array.
In computer science, a compressed suffix array is a compressed data structure for pattern matching. Compressed suffix arrays are a general class of data structure that improve on the suffix array. These data structures enable quick search for an arbitrary string with a comparatively small index. Given a text T of n characters from an alphabet Σ, a compressed suffix array supports searching for arbitrary patterns in T. For an input pattern P of m characters, the search time is typically O(m) or O(m + log(n)). The space used is typically O ( n H k ( T ) ) + o ( n ) {\displaystyle O(nH_{k}(T))+o(n)} , where H k ( T ) {\displaystyle H_{k}(T)} is the k-th order empirical entropy of the text T. The time and space to construct a compressed suffix array are normally O ( n ) {\displaystyle O(n)} . The original presentation of a compressed suffix array solved a long-standing open problem by showing that fast pattern matching was possible using only a linear-space data structure, namely, one proportional to the size of the text T, which takes O ( n log | Σ | ) {\displaystyle O(n\,{\log |\Sigma |})} bits. The conventional suffix array and suffix tree use Ω ( n log n ) {\displaystyle \Omega (n\,{\log n})} bits, which is substantially larger. The basis for the data structure is a recursive decomposition using the "neighbor function," which allows a suffix array to be represented by one of half its length. The construction is repeated multiple times until the resulting suffix array uses a linear number of bits. Following work showed that the actual storage space was related to the 0 t h {\displaystyle 0^{th}} -order entropy and that the index supports self-indexing. The space bound was further improved achieving the ultimate goal of higher-order entropy; the compression is obtained by partitioning the neighbor function by high-order contexts, and compressing each partition with a wavelet tree. The space usage is extremely competitive in practice with other state-of-the-art compressors, and it also supports fast in-situ pattern matching. The memory accesses made by compressed suffix arrays and other compressed data structures for pattern matching are typically not localized, and thus these data structures have been notoriously hard to design efficiently for use in external memory. Recent progress using geometric duality takes advantage of the block access provided by disks to speed up the I/O time significantly In addition, potentially practical search performance for a compressed suffix array in external-memory has been demonstrated.
In computer science, a generalized suffix array (GSA) is a suffix array containing all suffixes for a set of strings. Given the set of strings S = S 1 , S 2 , S 3 , . . . , S k {\displaystyle S=S_{1},S_{2},S_{3},...,S_{k}} of total length n {\displaystyle n} , it is a lexicographically sorted array of all suffixes of each string in S {\displaystyle S} . It is primarily used in bioinformatics and string processing.
A suffix is part of a word; an affix that follows the morphemes to which it can attach. Possessive suffix, a suffix used in word formation for creation of various possessive forms Suffix may also refer to: Suffix (name), the style at the end of a person's name which gives additional identifying information about the person Suffix (computer science), the last part of a string of characters Suffix notation, a notation for manipulating vector quantities, also known as index notation Suffix array, an array of integers giving the starting positions of suffixes of a string in lexicographical order Suffix tree, a data structure that presents the suffixes of a given string in a way that allows for a particularly fast implementation of many important string operations
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Madam C.J. Walker
