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Kirkpatrick–Seidel Algorithm
The Kirkpatrick–Seidel algorithm, proposed by its authors as a potential "ultimate planar convex hull algorithm", is an algorithm for computing the convex hull of a set of points in the plane, with \mathcal(n \log h) time complexity, where n is the number of input points and h is the number of points (non dominated or maximal points, as called in some texts) in the hull. Thus, the algorithm is output-sensitive: its running time depends on both the input size and the output size. Another output-sensitive algorithm, the gift wrapping algorithm, was known much earlier, but the Kirkpatrick–Seidel algorithm has an asymptotic running time that is significantly smaller and that always improves on the \mathcal(n \log n) bounds of non-output-sensitive algorithms. The Kirkpatrick–Seidel algorithm is named after its inventors, David G. Kirkpatrick and Raimund Seidel. Although the algorithm is asymptotically optimal, it is not very practical for moderate-sized problems. Algorithm The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Convex Hull
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Analysis Of Algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Output-sensitive Algorithm
In computer science, an output-sensitive algorithm is an algorithm whose running time depends on the size of the output, instead of, or in addition to, the size of the input. For certain problems where the output size varies widely, for example from linear in the size of the input to quadratic in the size of the input, analyses that take the output size explicitly into account can produce better runtime bounds that differentiate algorithms that would otherwise have identical asymptotic complexity. Examples Division by subtraction A simple example of an output-sensitive algorithm is given by the division algorithm ''division by subtraction'' which computes the quotient and remainder of dividing two positive integers using only addition, subtraction, and comparisons: def divide(number: int, divisor: int) -> Tuple nt, int """Division by subtraction.""" if not divisor: raise ZeroDivisionError if number >> divide(10, 2) (5, 0) >>> divide(10, 3) (3, 1) This a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Gift Wrapping Algorithm
In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. Planar case In the two-dimensional case the algorithm is also known as Jarvis march, after R. A. Jarvis, who published it in 1973; it has O(''nh'') time complexity, where ''n'' is the number of points and ''h'' is the number of points on the convex hull. Its real-life performance compared with other convex hull algorithms is favorable when n is small or h is expected to be very small with respect to n. In general cases, the algorithm is outperformed by many others ( See Convex hull algorithms). Algorithm For the sake of simplicity, the description below assumes that the points are in general position, i.e., no three points are collinear. The algorithm may be easily modified to deal with collinearity, including the choice whether it should report only extreme points (vertices of the convex hull) or all points that lie on the convex hull. Also, the comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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David G
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Raimund Seidel
Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry. Seidel was born in Graz, Austria, and studied with Hermann Maurer at the Graz University of Technology. He received his M. Sc. in 1981 from University of British Columbia under David G. Kirkpatrick. He received his Ph.D. in 1987 from Cornell University under the supervision of John Gilbert. After teaching at the University of California, Berkeley, he moved in 1994 to Saarland University. In 1997 he and Christoph M. Hoffmann were program chairs for the Symposium on Computational Geometry. In 2014, he took over as Scientific Director of the Leibniz Center for Informatics (LZI) from Reinhard Wilhelm. Seidel invented backwards analysis of randomized algorithms and used it to analyze a simple linear programming algorithm that runs in linear time for problems of bounded dimension. With his student Cecilia R. Aragon in 1989 he devised the treap data structure I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References * External linksSIAM Journal on Computing on |
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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 cos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Franco P
Franco may refer to: Name * Franco (name) * Francisco Franco (1892–1975), Spanish general and dictator of Spain from 1939 to 1975 * Franco Luambo (1938–1989), Congolese musician, the "Grand Maître" Prefix * Franco, a prefix used when referring to France, a country * Franco, a prefix used when referring to French people and their diaspora, e.g. Franco-Americans, Franco-Mauritians * Franco, a prefix used when referring to Franks, a West Germanic tribe Places * El Franco, a municipality of Asturias in Spain * Presidente Franco District, in Paraguay * Franco, Virginia, an unincorporated community, in the United States Other uses * Franco (band), Filipino band * Franco (''General Hospital''), a fictional character on the American soap opera ''General Hospital'' * Franco, the Luccan franc, a 19th-century currency of Lucca, Italy * ''Franco, Ciccio e il pirata Barbanera'', a 1969 Italian comedy film directed by Mario Amendola * ''Franco, ese hombre'', a 1964 documentary f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Recursively
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references ("crock recursion") can occur. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ''ancestor''. One's anc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Bitangent
In geometry, a bitangent to a curve is a line that touches in two distinct points and and that has the same direction as at these points. That is, is a tangent line at and at . Bitangents of algebraic curves In general, an algebraic curve will have infinitely many secant lines, but only finitely many bitangents. Bézout's theorem implies that an algebraic plane curve with a bitangent must have degree at least 4. The case of the 28 bitangents of a quartic was a celebrated piece of geometry of the nineteenth century, a relationship being shown to the 27 lines on the cubic surface. Bitangents of polygons The four bitangents of two disjoint convex polygons may be found efficiently by an algorithm based on binary search in which one maintains a binary search pointer into the lists of edges of each polygon and moves one of the pointers left or right at each steps depending on where the tangent lines to the edges at the two pointers cross each other. This bitangent ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |