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Massively Parallel Communication
In the study of parallel algorithms, the massively parallel communication model or MPC model is a theoretical model of computing, intended as an abstraction for parallel computing systems that use frameworks such as MapReduce, and frequently applied to algorithmic problems in graph theory. Model In this model, one is given a system consisting of M machines, each having a local memory consisting of S words of memory. The input to a computational problem in this model is distributed arbitrarily across all of the machines, and is assumed to have a size N at most proportional to MS. Typically one assumes that S=N^, for some parameter \varepsilon>0, so that each machine can see only a small fraction of the input and some nontrivial level of parallelism will be required to solve the given problem. With this setup, computation proceeds in a sequence of rounds. In each round, each machine performs some local computation with the information it has in its memory, and then exchanges mess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Algorithm
In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can do multiple operations in a given time. It has been a tradition of computer science to describe serial algorithms in abstract machine models, often the one known as random-access machine. Similarly, many computer science researchers have used a so-called parallel random-access machine (PRAM) as a parallel abstract machine (shared-memory). Many parallel algorithms are executed concurrently – though in general concurrent algorithms are a distinct concept – and thus these concepts are often conflated, with which aspect of an algorithm is parallel and which is concurrent not being clearly distinguished. Further, non-parallel, non-concurrent algorithms are often referred to as " sequential algorithms", by contrast with concurrent algorithms. Parallelizability Algorithms vary significantly in how parallelizable they are, ranging from easily parallelizable to compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MapReduce
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. A MapReduce program is composed of a ''map'' procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a '' reduce'' method, which performs a summary operation (such as counting the number of students in each queue, yielding name frequencies). The "MapReduce System" (also called "infrastructure" or "framework") orchestrates the processing by marshalling the distributed servers, running the various tasks in parallel, managing all communications and data transfers between the various parts of the system, and providing for redundancy and fault tolerance. The model is a specialization of the ''split-apply-combine'' strategy for data analysis. It is inspired by the map and reduce functions commonly used in functional programming,"Our abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulk Synchronous Parallel
The bulk synchronous parallel (BSP) abstract computer is a bridging model for designing parallel algorithms. It is similar to the parallel random access machine (PRAM) model, but unlike PRAM, BSP does not take communication and synchronization for granted. In fact, quantifying the requisite synchronization and communication is an important part of analyzing a BSP algorithm. History The BSP model was developed by Leslie Valiant of Harvard University during the 1980s. The definitive article was published in 1990.Leslie G. Valiant, A bridging model for parallel computation, Communications of the ACM, Volume 33 Issue 8, Aug. 199/ref> Between 1990 and 1992, Leslie Valiant and Bill McColl of Oxford University worked on ideas for a distributed memory BSP programming model, in Princeton and at Harvard. Between 1992 and 1997, McColl led a large research team at Oxford that developed various BSP programming libraries, languages and tools, and also numerous massively parallel BSP algorit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel RAM
In computer science, a parallel random-access machine (parallel RAM or PRAM) is a shared-memory abstract machine. As its name indicates, the PRAM is intended as the parallel-computing analogy to the random-access machine (RAM) (not to be confused with random-access memory). In the same way that the RAM is used by sequential-algorithm designers to model algorithmic performance (such as time complexity), the PRAM is used by parallel-algorithm designers to model parallel algorithmic performance (such as time complexity, where the number of processors assumed is typically also stated). Similar to the way in which the RAM model neglects practical issues, such as access time to cache memory versus main memory, the PRAM model neglects such issues as synchronization and communication, but provides any (problem-size-dependent) number of processors. Algorithm cost, for instance, is estimated using two parameters O(time) and O(time × processor_number). Read/write conflicts Read/write confli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. Although some algorithms are designed for sequential access, the highest-performing algorithms assum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Sample
In this statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population (in many cases, collecting the whole population is impossible, like getting sizes of all stars in the universe), and thus, it can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probabil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Butterfly Multitree
Butterflies are winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossils have been dated to the Paleocene, about 56 million years ago, though molecular evidence suggests that they likely originated in the Cretaceous. Butterflies have a four-stage life cycle, and like other holometabolous insects they undergo complete metamorphosis. Winged adults lay eggs on the food plant on which their larvae, known as caterpillars, will feed. The caterpillars grow, sometimes very rapidly, and when fully developed, pupate in a chrysalis. When metamorphosis is complete, the pupal skin splits, the adult insect climbs out, expands its wings to dry, and flies off. Some butterflies, especially in the tropics, have several generations in a year, while others have a single generation, and a few in cold locations may take several ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balanced Binary Search Tree
In computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions.Donald Knuth. ''The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Second Edition. Addison-Wesley, 1998. . Section 6.2.3: Balanced Trees, pp.458–481. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing". For height-balanced binary trees, the height is defined to be logarithmic O(\log n) in the number n of items. This is the case for many binary search trees, such as AVL trees and red–black trees. Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items. Self-balancin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
