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B-heap
A B-heap is a binary heap implemented to keep subtrees in a single page. This reduces the number of pages accessed by up to a factor of ten for big heaps when using virtual memory, compared with the traditional implementation. The traditional mapping of elements to locations in an array puts almost every level in a different page. There are other heap variants which are efficient in computers using virtual memory or caches, such as cache-oblivious algorithms, k-heaps, and van Emde Boas layouts. Motivation Traditionally, binary trees are laid out in consecutive memory according to a n -> rule, meaning that if a node is at position n, its left and right child are taken to be at positions 2n and 2n+1 in the array. The root is at position 1. A common operation on binary trees is the vertical traversal; stepping down through the levels of a tree in order to arrive at a searched node. However, because of the way memory is organized on modern computers into pages in virtual memory, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Heap
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: *Shape property: a binary heap is a ''complete binary tree''; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right. *Heap property: the key stored in each node is either greater than or equal to (≥) or less than or equal to (≤) the keys in the node's children, according to some total order. Heaps where the parent key is greater than or equal to (≥) the child keys are called ''max-heaps''; those where it is less than or equal to (≤) are called ''min-heaps''. Efficient (logarithmic time) algorithms are known for the two ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Page (computer Memory)
A page, memory page, or virtual page is a fixed-length contiguous block of virtual memory, described by a single entry in the page table. It is the smallest unit of data for memory management in a virtual memory operating system. Similarly, a page frame is the smallest fixed-length contiguous block of physical memory into which memory pages are mapped by the operating system. A transfer of pages between main memory and an auxiliary store, such as a hard disk drive, is referred to as paging or swapping. Page size trade-off Page size is usually determined by the processor architecture. Traditionally, pages in a system had uniform size, such as 4,096 bytes. However, processor designs often allow two or more, sometimes simultaneous, page sizes due to its benefits. There are several points that can factor into choosing the best page size. Page table size A system with a smaller page size uses more pages, requiring a page table that occupies more space. For example, if a 232 vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Memory
In computing, virtual memory, or virtual storage is a memory management technique that provides an "idealized abstraction of the storage resources that are actually available on a given machine" which "creates the illusion to users of a very large (main) memory". The computer's operating system, using a combination of hardware and software, maps memory addresses used by a program, called '' virtual addresses'', into ''physical addresses'' in computer memory. Main storage, as seen by a process or task, appears as a contiguous address space or collection of contiguous segments. The operating system manages virtual address spaces and the assignment of real memory to virtual memory. Address translation hardware in the CPU, often referred to as a memory management unit (MMU), automatically translates virtual addresses to physical addresses. Software within the operating system may extend these capabilities, utilizing, e.g., disk storage, to provide a virtual address space that ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ACM Queue
''ACM Queue'' is a bimonthly computer magazine founded and published by the Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ... (ACM). The magazine was established in 2003. Steve Bourne helped found the magazine when he was president of the ACM and is chair of the editorial board. The magazine is produced by computing professionals and is intended for computing professionals. It is available only in electronic form and is available on the Internet on subscription basis. Some of the articles published in ''Queue'' are also included in ACM's monthly magazine, ''Communications of the ACM'', in the Practitioner section. References External links Official website {{compu-mag-stub Computer magazines published in the United States Bimonthly magazin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Array Data Structure
In computer science, an array is a data structure consisting of a collection of ''elements'' (values or variables), each identified by at least one ''array index'' or ''key''. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index ''i'' has the address 2000 + (''i'' × 4). The memory address of the first element of an array is called first address, foundation address, or base address. Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache-oblivious Algorithm
In computing, a cache-oblivious algorithm (or cache-transcendent algorithm) is an algorithm designed to take advantage of a processor cache without having the size of the cache (or the length of the cache lines, etc.) as an explicit parameter. An optimal cache-oblivious algorithm is a cache-oblivious algorithm that uses the cache optimally (in an asymptotic sense, ignoring constant factors). Thus, a cache-oblivious algorithm is designed to perform well, without modification, on multiple machines with different cache sizes, or for a memory hierarchy with different levels of cache having different sizes. Cache-oblivious algorithms are contrasted with explicit ''loop tiling'', which explicitly breaks a problem into blocks that are optimally sized for a given cache. Optimal cache-oblivious algorithms are known for matrix multiplication, matrix transposition, sorting, and several other problems. Some more general algorithms, such as Cooley–Tukey FFT, are optimally cache-oblivious ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Computer Journal
''The Computer Journal'' is a peer-reviewed scientific journal covering computer science and information systems. Established in 1958, it is one of the oldest computer science research journals. It is published by Oxford University Press on behalf of BCS, The Chartered Institute for IT. The authors of the best paper in each annual volume receive the Wilkes Award from BCS, The Chartered Institute for IT. Editors-in-chief The following people have been editor-in-chief: * 1958–1969 Eric N. Mutch * 1969–1992 Peter Hammersley * 1993–2000 C. J. van Rijsbergen * 2000–2008 Fionn Murtagh * 2008–2012 Erol Gelenbe * 2012–2016 Fionn Murtagh * 2016–2020 Steve Furber Stephen Byram Furber (born 21 March 1953) is a British computer scientist, mathematician and hardware engineer, currently the ICL Professor of Computer Engineering in the Department of Computer Science at the University of Manchester, UK. A ... * 2021–present Tom Crick References External links Official ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Emde Boas Tree
A van Emde Boas tree (), also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with -bit integer keys. It was invented by a team led by Dutch computer scientist Peter van Emde Boas in 1975. It performs all operations in time (assuming that an bit operation can be performed in constant time), or equivalently in time, where is the largest element that can be stored in the tree. The parameter is not to be confused with the actual number of elements stored in the tree, by which the performance of other tree data-structures is often measured. The vEB tree has poor space efficiency. For example, for storing 32-bit integers (i.e., when ), it requires bits of storage. However, similar data structures with equally good time efficiency and space exist, where is the number of stored elements. Supported operations A vEB supports the operations of an ''ordered associative array'', which includes the usual associative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Systems Theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ''continuous dynamical systems''. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called ''discrete dynamical systems''. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations. This theory deals with the long-term qualitative behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (''L'', ''S'', ''R''), where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A ''cache hit'' occurs when the requested data can be found in a cache, while a ''cache miss'' occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective and to enable efficient use of data, caches must be relatively small. Nevertheless, caches have proven themselves in many areas of computing, because typical computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested already, and spatial locality, where d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M-ary Tree
In graph theory, an ''m''-ary tree (also known as ''n''-ary, ''k''-ary or ''k''-way tree) is a rooted tree in which each node has no more than ''m'' children. A binary tree is the special case where ''m'' = 2, and a ternary tree is another case with ''m'' = 3 that limits its children to three. Types of ''m''-ary trees * A full ''m''-ary tree is an ''m''-ary tree where within each level every node has either 0 or ''m'' children. * A complete ''m''-ary tree is an ''m''-ary tree which is maximally space efficient. It must be completely filled on every level except for the last level. However, if the last level is not complete, then all nodes of the tree must be "as far left as possible". * A perfect ''m''-ary tree is a full ''m''-ary tree in which all leaf nodes are at the same depth. Properties of ''m''-ary trees * For an ''m''-ary tree with height ''h'', the upper bound for the maximum number of leaves is m^h. * The height ''h ''of an ''m''-ary tree does not include the roo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
