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Cache-oblivious
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 und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divide-and-conquer Algorithm
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform (FFT). Designing efficient divide-and-conquer algorithms can be difficult. As in mathematical induction, it is often necessary to generalize the problem to make it amenable to a recursive solution. The correctness of a divide-and-conquer algorithm is usually proved by mathematical induction, and its computational cost is o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooley–Tukey FFT Algorithm
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size N = N_1N_2 in terms of ''N''1 smaller DFTs of sizes ''N''2, recursively, to reduce the computation time to O(''N'' log ''N'') for highly composite ''N'' (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below. Because the Cooley–Tukey algorithm breaks the DFT into smaller DFTs, it can be combined arbitrarily with any other algorithm for the DFT. For example, Rader's or Bluestein's algorithm can be used to handle large prime factors that cannot be decomposed by Cooley–Tukey, or the prime-factor algorithm can be exploited for greater efficiency in separating out relatively prime factors. The algorithm, along with its recursive application, was invented by Carl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Funnelsort
Funnelsort is a comparison-based sorting algorithm. It is similar to mergesort, but it is a cache-oblivious algorithm, designed for a setting where the number of elements to sort is too large to fit in a cache where operations are done. It was introduced by Matteo Frigo, Charles Leiserson, Harald Prokop, and Sridhar Ramachandran in 1999 in the context of the cache oblivious model. Mathematical properties In the external memory model, the number of memory transfers it needs to perform a sort of N items on a machine with cache of size Z and cache lines of length L is O \left(\tfrac \log_ N \right), under the tall cache assumption that Z = \Omega(L^2). This number of memory transfers has been shown to be asymptotically optimal for comparison sorts. Funnelsort also achieves the asymptotically optimal runtime complexity of \Theta(N \log N). Algorithm Basic overview Funnelsort operates on a contiguous array of N elements. To sort the elements, it performs the following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Tiling
In computer science and particularly in compiler design, loop nest optimization (LNO) is an optimization technique that applies a set of loop transformations for the purpose of locality optimization or parallelization or another loop overhead reduction of the loop nests. (Nested loops occur when one loop is inside of another loop.) One classical usage is to reduce memory access latency or the cache bandwidth necessary due to cache reuse for some common linear algebra algorithms. The technique used to produce this optimization is called loop tiling, also known as loop blocking or strip mine and interchange. Overview Loop tiling partitions a loop's iteration space into smaller chunks or blocks, so as to help ensure data used in a loop stays in the cache until it is reused. The partitioning of loop iteration space leads to partitioning of a large array into smaller blocks, thus fitting accessed array elements into cache size, enhancing cache reuse and eliminating cache size requir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache-oblivious Matrix Multiplication
Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network). Directly applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of field operations to multiply two matrices over that field ( in big O notation). Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that is, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
External Memory Model
In computing, external memory algorithms or out-of-core algorithms are algorithms that are designed to process data that are too large to fit into a computer's main memory at once. Such algorithms must be optimized to efficiently fetch and access data stored in slow bulk memory (auxiliary memory) such as hard drives or tape drives, or when memory is on a computer network. External memory algorithms are analyzed in the external memory model. Model External memory algorithms are analyzed in an idealized model of computation called the external memory model (or I/O model, or disk access model). The external memory model is an abstract machine similar to the RAM machine model, but with a cache in addition to main memory. The model captures the fact that read and write operations are much faster in a cache than in main memory, and that reading long contiguous blocks is faster than reading randomly using a disk read-and-write head. The running time of an algorithm in the external memor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harald Prokop
Harald Prokop is the Chief Technical Officer of SCVNGR, parent company of LevelUp, as of April 2012. He worked at Akamai Technologies from 1999 to 2012, where he was Senior Vice President of Engineering and is also known for having elucidated the concept of the 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 o .... References Living people Year of birth missing (living people) {{Business-bio-stub ... [...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] |
Block (data Storage)
In computing (specifically data transmission and data storage), a block, sometimes called a physical record, is a sequence of bytes or bits, usually containing some whole number of records, having a maximum length; a ''block size''. Data thus structured are said to be ''blocked''. The process of putting data into blocks is called ''blocking'', while ''deblocking'' is the process of extracting data from blocks. Blocked data is normally stored in a data buffer, and read or written a whole block at a time. Blocking reduces the overhead and speeds up the handling of the data stream. For some devices, such as magnetic tape and CKD disk devices, blocking reduces the amount of external storage required for the data. Blocking is almost universally employed when storing data to 9-track magnetic tape, NAND flash memory, and rotating media such as floppy disks, hard disks, and optical discs. Most file systems are based on a block device, which is a level of abstraction for the hardwar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blitz++
Blitz++ is a high-performance vector mathematics library written in C++. This library is intended for use in scientific applications that might otherwise be implemented with Fortran or MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation .... Blitz++ utilizes advanced C++ template metaprogramming techniques, including expression templates, to provide speed-optimized mathematical operations on sequences of data without sacrificing the natural syntax provided by other mathematical programming systems. Indeed, it has been recognized as a pioneer in the area of C++ template metaprogramming. David Abrahams, Aleksey Gurtovoy: ''C++ Template Metaprogramming: Concepts, Tools, and Techniques from Boost and Beyond'', Addison-Wesley, References External links *{{Official website, http ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Machine
An abstract machine is a computer science theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is analogous to a mathematical function in that it receives inputs and produces outputs based on predefined rules. Abstract machines vary from literal machines in that they are expected to perform correctly and independently of hardware. Abstract machines are “machines” because they allow step-by-step execution of programmes; they are “ abstract” because they ignore many aspects of actual ( hardware) machines. A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter. They can be used for purely theoretical reasons as well as models for real-world computer systems. In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyse the complexity of algorithms. This use of abstr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Models Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite state machines * Post machines (Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model Functional models Functional models include: * Abstract re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
