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Real RAM
In computing, especially computational geometry, a real RAM (random-access machine) is a mathematical model of a computer that can compute with exact real numbers instead of the binary fixed point or floating point numbers used by most actual computers. The real RAM was formulated by Michael Ian Shamos in his 1978 Ph.D. dissertation. Model The "RAM" part of the real RAM model name stands for "random-access machine". This is a model of computing that resembles a simplified version of a standard computer architecture. It consists of a stored program, a computer memory unit consisting of an array of cells, and a central processing unit with a bounded number of registers. Each memory cell or register can store a real number. Under the control of the program, the real RAM can transfer real numbers between memory and registers, and perform arithmetic operations on the values stored in the registers. The allowed operations typically include addition, subtraction, multiplication, and di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Analysis of algorithms, Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(''n''2) and O(''n'' log ''n'') may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (Computer-aided design, CAD/Compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Library
In computer science, a library is a collection of non-volatile resources used by computer programs, often for software development. These may include configuration data, documentation, help data, message templates, pre-written code and subroutines, classes, values or type specifications. In IBM's OS/360 and its successors they are referred to as partitioned data sets. A library is also a collection of implementations of behavior, written in terms of a language, that has a well-defined interface by which the behavior is invoked. For instance, people who want to write a higher-level program can use a library to make system calls instead of implementing those system calls over and over again. In addition, the behavior is provided for reuse by multiple independent programs. A program invokes the library-provided behavior via a mechanism of the language. For example, in a simple imperative language such as C, the behavior in a library is invoked by using C's normal function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classes Of Computers
Computers can be classified, or typed, in many ways. Some common classifications of computers are given below. Classes by purpose , - , style="text-align: left;", Notes: Microcomputers (personal computers) Microcomputers became the most common type of computer in the late 20th century. The term “microcomputer” was introduced with the advent of systems based on single-chip microprocessors. The best-known early system was the Altair 8800, introduced in 1975. The term "microcomputer" has practically become an anachronism as it has fallen into disuse. These computers include: * Desktop computers – A case put under or on a desk. The display may be optional, depending on use. The case size may vary, depending on the required expansion slots. Very small computers of this kind may be integrated into the monitor. * Rackmount computers – The cases of these computers fit into 19-inch racks, and maybe space-optimized and very flat. A dedicated display, keyboar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perles Configuration
In geometry, the Perles configuration is a system of nine points and nine lines in the Euclidean plane for which every combinatorially equivalent realization has at least one irrational number as one of its coordinates. It can be constructed from the diagonals and symmetry lines of a regular pentagon, omitting one of the symmetry lines. In turn, it can be used to construct higher-dimensional convex polytopes that cannot be given rational coordinates, having the fewest vertices of any known example. All of the realizations of the Perles configuration in the projective plane are equivalent to each other under projective transformations. Construction One way of constructing the Perles configuration is to start with a regular pentagon and its five diagonals. These diagonals form the sides of a smaller inner pentagon nested inside the outer pentagon. Each vertex of the outer pentagon is situated opposite from a vertex of the inner pentagon. The nine points of the configuration consis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Sort
A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator forms a total preorder over the data, with: # if ''a'' ≤ ''b'' and ''b'' ≤ ''c'' then ''a'' ≤ ''c'' (transitivity) # for all ''a'' and ''b'', ''a'' ≤ ''b'' or ''b'' ≤ ''a'' ( connexity). It is possible that both ''a'' ≤ ''b'' and ''b'' ≤ ''a''; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. A metaphor for thinking about comparison sorts is that someone has a set of unlabelled weights and a balance scale. Their goal is to line up the weights in order by their weight without any information except that obtained by placing two weights on the scale and seeing which one i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Sorting
In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers, or text strings.. The ability to perform integer arithmetic on the keys allows integer sorting algorithms to be faster than comparison sorting algorithms in many cases, depending on the details of which operations are allowed in the model of computing and how large the integers to be sorted are. Integer sorting algorithms including pigeonhole sort, counting sort, and radix sort are widely used and practical. Other integer sorting algorithms with smaller worst-case time bounds are not believed to be practical for computer architectures with 64 or fewer bits per word. Many such algorithms are known, with performance depending on a combination of the number of items to be sorted, number of bits per key, and number of bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word RAM
In theoretical computer science, the word RAM (word random-access machine) model is a model of computation in which a random-access machine does bitwise operations on a word of bits. Michael Fredman and Dan Willard created it in 1990 to simulate programming languages like C. Model The word RAM model is an abstract machine similar to a random-access machine, but with additional capabilities. It works with words of size up to bits, meaning it can store integers up to size 2^w. Because the model assumes that the word size matches the problem size, that is, for a problem of size , w \ge \log n, the word RAM model is a transdichotomous model. The model allows bitwise operations such as arithmetic and logical shifts to be done in constant time. The number of possible values is , where U \le 2^w. Algorithms and data structures In the word RAM model, integer sorting can be done fairly efficiently. Yijie Han and Mikkel Thorup created a randomized algorithm to sort integers in expected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-completeness
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a deter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blum–Shub–Smale Machine
In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is a Random Access Machine with registers that can store arbitrary real numbers and that can compute rational functions over reals in a single time step. It is often referred to as Real RAM model. BSS machines are more powerful than Turing machines, because the latter are by definition restricted to a finite alphabet. A Turing machine can be empowered to store arbitrary rational numbers in a single tape symbol by making that finite alphabet arbitrarily large (in terms of a physical machine using transistor-based memory, building its memory locations of enough transistors to store the desired number), but this does not extend to the uncountable real numbers (for example, no number of transistors can accurately represent Pi). Definition A BSS mach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Library Of Efficient Data Types And Algorithms
The Library of Efficient Data types and Algorithms (LEDA) is a proprietarily-licensed software library providing C++ implementations of a broad variety of algorithms for graph theory and computational geometry.. It was originally developed by the Max Planck Institute for Informatics Saarbrücken. Since 2001, LEDA is further developed and distributed by the Algorithmic Solutions Software GmbH. LEDA is available as Free, Research, and Professional edition. The Free edition is freeware, with source code access available for purchase. The Research and Professional editions require payment of licensing fees for any use. Since October 2017, LEDA graph algorithms are also available for Java development environment. Technical details Data types Numerical representations LEDA provides four additional numerical representations alongside those built-in to C++: integer, rational, bigfloat, and real: *LEDA's integer type offers an improvement over the built-in int datatype by elimina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
