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Generalized Suffix Tree
In computer science, a generalized suffix tree is a suffix tree for a set of strings. Given the set of strings D=S_1,S_2,\dots,S_d of total length n, it is a Patricia tree containing all n suffixes of the strings. It is mostly used in bioinformatics. Functionality It can be built in \Theta(n) time and space, and can be used to find all occurrences of a string of length in O(m + z) time, which is asymptotically optimal (assuming the size of the alphabet is constant). When constructing such a tree, each string should be padded with a unique out-of-alphabet marker symbol (or string) to ensure no suffix is a substring of another, guaranteeing each suffix is represented by a unique leaf node. Algorithms for constructing a GST include Ukkonen's algorithm (1995) and McCreight's algorithm (1976). Example A suffix tree for the strings ABAB and BABA is shown in a figure above. They are padded with the unique terminator strings $0 and $1. The numbers in the leaf nodes are string num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Suffix Tree ABAB BABA
In linguistics, a suffix is an affix which is placed after the stem of a word. Common examples are case endings, which indicate the grammatical case of nouns and adjectives, and verb endings, which form the conjugation of verbs. Suffixes can carry grammatical information (inflectional endings) or lexical information ( derivational/lexical suffixes)''.'' Inflection changes the grammatical properties of a word within its syntactic category. Derivational suffixes fall into two categories: class-changing derivation and class-maintaining derivation. Particularly in the study of Semitic languages, suffixes are called affirmatives, as they can alter the form of the words. In Indo-European studies, a distinction is made between suffixes and endings (see Proto-Indo-European root). A word-final segment that is somewhere between a free morpheme and a bound morpheme is known as a suffixoidKremer, Marion. 1997. ''Person reference and gender in translation: a contrastive investigation of Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Suffix Tree
In computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particularly fast implementations of many important string operations. The construction of such a tree for the string S takes time and space linear in the length of S. Once constructed, several operations can be performed quickly, such as locating a substring in S, locating a substring if a certain number of mistakes are allowed, and locating matches for a regular expression pattern. Suffix trees also provided one of the first linear-time solutions for the longest common substring problem. These speedups come at a cost: storing a string's suffix tree typically requires significantly more space than storing the string itself. History The concept was first introduced by . Rather than the suffix S ..n/math>, Weiner stored in his trie the ''prefix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
String (computer Science)
In computer programming, a string is traditionally a sequence of character (computing), characters, either as a literal (computer programming), literal constant or as some kind of Variable (computer science), variable. The latter may allow its elements to be Immutable object, mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or word (computer architecture), words) that stores a sequence of elements, typically characters, using some character encoding. More general, ''string'' may also denote a sequence (or List (abstract data type), list) of data other than just characters. Depending on the programming language and precise data type used, a variable (programming), variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Patricia Tree
In computer science, a radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which each node that is the only child is merged with its parent. The result is that the number of children of every internal node is at most the radix of the radix tree, where = 2 for some integer ≥ 1. Unlike regular trees, edges can be labeled with sequences of elements as well as single elements. This makes radix trees much more efficient for small sets (especially if the strings are long) and for sets of strings that share long prefixes. Unlike regular trees (where whole keys are compared ''en masse'' from their beginning up to the point of inequality), the key at each node is compared chunk-of-bits by chunk-of-bits, where the quantity of bits in that chunk at that node is the radix of the radix trie. When is 2, the radix trie is binary (i.e., compare that node's 1-bit portion of the key), which minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Suffix (computer Science)
In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "''the best of''" is a substring of "''It was the best of times''". In contrast, "''Itwastimes''" is a subsequence of "''It was the best of times''", but not a substring. Prefixes and suffixes are special cases of substrings. A prefix of a string S is a substring of S that occurs at the beginning of S; likewise, a suffix of a string S is a substring that occurs at the end of S. The substrings of the string "''apple''" would be: "''a''", "''ap''", "''app''", "''appl''", "''apple''", "''p''", "''pp''", "''ppl''", "''pple''", "''pl''", "''ple''", "''l''", "''le''" "''e''", "" (note the empty string at the end). Substring A string u is a substring (or factor) of a string t if there exists two strings p and s such that t = pus. In particular, the empty string is a substring of every string. Example: The string u=ana is equal to substrings (and subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bioinformatics
Bioinformatics () is an interdisciplinary field of science that develops methods and Bioinformatics software, software tools for understanding biological data, especially when the data sets are large and complex. Bioinformatics uses biology, chemistry, physics, computer science, data science, computer programming, information engineering, mathematics and statistics to analyze and interpret biological data. The process of analyzing and interpreting data can sometimes be referred to as computational biology, however this distinction between the two terms is often disputed. To some, the term ''computational biology'' refers to building and using models of biological systems. Computational, statistical, and computer programming techniques have been used for In silico, computer simulation analyses of biological queries. They include reused specific analysis "pipelines", particularly in the field of genomics, such as by the identification of genes and single nucleotide polymorphis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Asymptotically Optimal
In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm. It is a term commonly encountered in computer science research as a result of widespread use of big-O notation. More formally, an algorithm is asymptotically optimal with respect to a particular resource if the problem has been proven to require of that resource, and the algorithm has been proven to use only These proofs require an assumption of a particular model of computation, i.e., certain restrictions on operations allowable with the input data. As a simple example, it's known that all comparison sorts require at least comparisons in the average and worst cases. Mergesort and heapsort are comparison sorts which perform comparisons, so they are asymptotically optimal in this sense. If the input data have some ''a priori'' properties which can be exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ukkonen's Algorithm
In computer science, Ukkonen's algorithm is a linear-time, online algorithm for constructing suffix tree In computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particu ...s, proposed by Esko Ukkonen in 1995. The algorithm begins with an implicit suffix tree containing the first character of the string. Then it steps through the string, adding successive characters until the tree is complete. This order addition of characters gives Ukkonen's algorithm its "on-line" property. The original algorithm presented by Peter Weiner proceeded backward from the last character to the first one from the shortest to the longest suffix. A simpler algorithm was found by Edward M. McCreight, going from the longest to the shortest suffix. Implicit suffix tree While generating suffix tree using Ukkonen's algorithm, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Suffix Array
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 as a simple, space efficient alternative to suffix trees. They had independently been discovered by Gaston Gonnet in 1987 under the name ''PAT array'' . gave the first in-place \mathcal(n) time suffix array construction algorithm that is optimal both in time and space, where ''in-place'' means that the algorithm only needs \mathcal(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. Definition Let S=S ..S /math> be an n-string and let S ,j/math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Trees (data Structures)
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
