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LCP Array
In computer science, the longest common prefix array (LCP Array data structure, array) is an auxiliary data structure to the suffix array. It stores the lengths of the longest common prefixes (LCPs) between all pairs of consecutive suffixes in a sorted suffix array. For example, if ''A'' := [aab, ab, abaab, b, baab] is a suffix array, the longest common prefix between ''A''[1] = aab and ''A''[2] = ab is ''a'' which has length 1, so ''H''[2] = 1 in the LCP array ''H''. Likewise, the LCP of ''A''[2] = ab and ''A''[3] = abaab is ab, so ''H''[3] = 2. Augmenting the suffix array with the LCP array allows one to efficiently simulate top-down and bottom-up Tree traversal, traversals of the suffix tree, speeds up pattern matching on the suffix array and is a prerequisite for compressed suffix trees. History The LCP array was introduced in 1993, by Udi Manber and Gene Myers alongside the suffix array in order to improve the running time of their string search algorithm. Definition Le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Data Structures
This is a list of well-known data structures. For a wider list of terms, see list of terms relating to algorithms and data structures. For a comparison of running times for a subset of this list see comparison of data structures. Data types Primitive types * Boolean, true or false. * Character *Floating-point representation of a finite subset of the rationals. ** Including single-precision and double-precision IEEE 754 floats, among others * Fixed-point representation of the rationals *Integer, a direct representation of either the integers or the non-negative integers *Reference, sometimes erroneously referred to as a pointer or handle, is a value that refers to another value, possibly including itself *Symbol, a unique identifier *Enumerated type, a set of symbols *Complex, representation of complex numbers Composite types or non-primitive type * Array, a sequence of elements of the same type stored contiguously in memory * Record (also called a structure or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicographic Order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into Sequence#Increasing_and_decreasing, increasing sequences, to which the lexicographical order is applied. A generalization defines an order on an ''n''-ary Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. Definition The words in a lexicon (the set of words u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrays
An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the sums of their horizontal segments form a succession of twelve-tone aggregates * Array mbira, a musical instrument * Spiral array model, a music pitch space Science Astronomy A telescope array, also called astronomical interferometer. Biology * Various kinds of multiple biological arrays called microarrays * Visual feature array, a model for the visual cortex Computer science Generally, a collection of same type data items that can be selected by indices computed at run-time, including: * Array (data structure), an arrangement of items at equally spaced addresses in computer memory * Array (data type), used in a programming language to specify a variable that can be indexed * Associative array, an abstract data structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burrows–Wheeler Transform
The Burrows–Wheeler transform (BWT) rearranges a character string into runs of similar characters, in a manner that can be reversed to recover the original string. Since compression techniques such as move-to-front transform and run-length encoding are more effective when such runs are present, the BWT can be used as a preparatory step to improve the efficiency of a compression algorithm, and is used this way in software such as bzip2. The algorithm can be implemented efficiently using a suffix array thus reaching linear time complexity. It was invented by David Wheeler in 1983, and later published by him and Michael Burrows in 1994. Their paper included a compression algorithm, called the Block-sorting Lossless Data Compression Algorithm or BSLDCA, that compresses data by using the BWT followed by move-to-front coding and Huffman coding or arithmetic coding. Description The transform is done by constructing a matrix (known as the Burrows-Wheeler Matrix) whose rows are the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructing The Suffix Tree Of Banana Based On The Suffix Array And The LCP Array - Case 2
Construction are processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life. It typically starts with planning, financing, and design that continues until the asset is built and ready for use. Construction also covers repairs and maintenance work, any works to expand, extend and improve the asset, and its eventual demolition, dismantling or decommissioning. The construction industry contributes significantly to many countries' gross domestic products (GDP). Global expenditure on construction activities was about $4 trillion in 2012. In 2022, expenditure on the construction industry exceeded $11 trillion a year, equivalent to about 13 percent of global GDP. This spending was forecasted to rise to around $14.8 trillion in 2030. The construction industry promotes economic development and brings many non-monetary benefits to many countries, but it is one of the most hazardous industries. For exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longest Repeated Substring Problem
In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space \Theta(n) by building a suffix tree In computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particu ... for the string (with a special end-of-string symbol like '$' appended), and finding the deepest internal node in the tree with more than one child. Depth is measured by the number of characters traversed from the root. The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LZ77 And LZ78
LZ77 and LZ78 are the two lossless data compression algorithms published in papers by Abraham Lempel and Jacob Ziv in 1977 and 1978. They are also known as Lempel-Ziv 1 (LZ1) and Lempel-Ziv 2 (LZ2) respectively. These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others. Besides their academic influence, these algorithms formed the basis of several ubiquitous compression schemes, including GIF and the DEFLATE algorithm used in PNG and ZIP. They are both theoretically dictionary coders. LZ77 maintains a sliding window during compression. This was later shown to be equivalent to the ''explicit dictionary'' constructed by LZ78—however, they are only equivalent when the entire data is intended to be decompressed. Since LZ77 encodes and decodes from a sliding window over previously seen characters, decompression must always start at the beginning of the input. Conceptually, LZ78 decompression could allow random access to the input if the en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowest Common Ancestor
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes and in a Tree (graph theory), tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from , is the lowest common ancestor). The LCA of and in is the shared ancestor of and that is located farthest from the root. Computation of lowest common ancestors may be useful, for instance, as part of a procedure for determining the distance between pairs of nodes in a tree: the distance from to can be computed as the distance from the root to , plus the distance from the root to , minus twice the distance from the root to their lowest common ancestor . In a tree data structure where each node points to its parent, the lowest common ancestor can be easily determined by finding the first intersection of the paths from and to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Minimum Query
In computer science, a range minimum query (RMQ) solves the problem of finding the minimal value in a sub-array of an array of comparable objects. Range minimum queries have several use cases in computer science, such as the lowest common ancestor problem and the longest common prefix problem (LCP). Definition Given an array of objects taken from a totally ordered set, such as integers, the range minimum query (with ) returns the position of the minimal element in the specified sub-array . For example, when , then the answer to the range minimum query for the sub-array is , as . Algorithms Naive solution In a typical setting, the array is static, i.e., elements are not inserted or deleted during a series of queries, and the queries to be answered on-line (i.e., the whole set of queries are not known in advance to the algorithm). In this case a suitable preprocessing of the array into a data structure ensures faster query answering. A naive solution is to precompu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Traversal
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a Tree (data structure), tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well. Types Unlike linked lists, one-dimensional arrays and other List of data structures#Linear data structures, linear data structures, which are canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in Depth-first search, depth-first or Breadth-first search, breadth-first order. There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex or hybrid schemes are possible, such as depth-limited searche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gene Myers
Eugene Wimberly "Gene" Myers Jr. (born December 31, 1953) is an American computer scientist and bioinformatician, who is best known for contributing to the early development of the NCBI's BLAST tool for sequence analysis. Education Myers received his Bachelor of Science in mathematics from the California Institute of Technology and a Doctor of Philosophy in computer science from the University of Colorado. Research Myers' 1990 paper (with Stephen Altschul and others) describing BLAST has received over 62,000+ citations making it amongst the most highly cited papers ever. Along with Udi Manber, Myers invented the suffix array data structure. Myers was a member of the faculty of the University of Arizona, the Vice President of Informatics Research at Celera Genomics, and a member of the faculty at UC Berkeley. At Celera Genomics, Myers was involved in the sequencing of the human genome, as well as the genomes of ''Drosophila'' and mouse. In particular, Myers advocated the use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
