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Maximal Empty Rectangle
In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic formulation, in particular, depending on the measure of the "size", domain (type of obstacles), and the orientation of the rectangle. The problems of this kind arise e.g., in electronic design automation, in design and verification of physical layout of integrated circuits. A maximal empty rectangle is a rectangle which is not contained in another empty rectangle. Each side of a maximal empty rectangle abuts an obstacle (otherwise the side may be shifted outwards, increasing the empty rectangle). An application of this kind is enumeration of "maximal white rectangles" in image segmentation R&D of image processing and pattern recognition. In the contexts of many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Empty Rectangle
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subhash Suri
Subhash Suri (born July 7, 1960) is an Indian-American computer scientist, a professor at the University of California, Santa Barbara. He is known for his research in computational geometry, computer networks, and algorithmic game theory. Biography Suri did his undergraduate studies at the Indian Institute of Technology Roorkee, graduating in 1981. He then worked as a programmer in India before beginning his graduate studies in 1984 at Johns Hopkins University, where he earned a Ph.D. in computer science in 1987 under the supervision of Joseph O'Rourke. He was a member of the technical staff at Bellcore until 1994, when he returned to academia as an associate professor at Washington University in St. Louis. He moved to a full professorship at UCSB in 2000.Curriculum vitae , retrieved 2012-03-12. He was program committee chair for the 7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Bounding Box
In geometry, the minimum or smallest bounding or enclosing box for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box". The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation. The terms "box" and "hyperrectangle" come from their usage in the Cartesian coordinate system, where they are indeed visualized as a rectangle (two-dimensional case), rectangular parallelepiped (three-dimensional case), etc. In the two-dimensional case it is called the minimum bounding rectangle. Axis-aligned minimum bounding box The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the constraint that the edges of the box are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Empty Sphere
In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in ''d''-dimensional space whose interior does not overlap with any given obstacles. Two dimensions The largest empty circle problem is the problem of finding a circle of largest radius in the plane whose interior does not overlap with any given obstacles. A common special case is as follows. Given ''n'' points in the plane, find a largest circle centered within their convex hull and enclosing none of them. The problem may be solved using Voronoi diagrams in optimal time \Theta(n\, \log\, n).Megan Schuster"The Largest Empty Circle Problem"/ref> See also *Bounding sphere *Farthest-first traversal *Largest empty rectangle In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron, whose polyhedral graph is the same as that of a cube. Special cases are a cube, with 6 squares as faces, a rectangular prism, rectangular cuboid or rectangular box, with 6 rectangles as faces, for both, cube and rectangular prism, adjacent faces meet in a right angle. General cuboids By Euler's formula the numbers of faces ''F'', of vertices ''V'', and of edges ''E'' of any convex polyhedron are related by the formula ''F'' + ''V'' = ''E'' + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges. Along with the rectangular cuboids, any parallelepiped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isothetic Polygon
An isothetic polygon is a polygon whose alternate sides belong to two parametric families of straight lines which are pencils of lines with centers at two points (possibly the point at infinity). The most well-known example of isothetic polygons are rectilinear polygons, and the former term is commonly used as a synonym for the latter one. Etymology and history The term is produced from Greek roots: '' iso-'' for "equal, same, similar" and (position, placement), i.e., the term is supposed to mean "polygon with similarly placed sides". The term was suggested during the early years of the computational geometry. Much emphasis was placed on the development of efficient algorithms for operations with orthogonal polygons, since the latter ones had an important application: representation of shapes in integrated circuit mask layouts due to their simplicity for design and manufacturing. It was observed that the efficiency of many geometric algorithms for orthogonal polygons does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *''Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *''Lecture Notes in Physics'' *''Lecture Notes in Mathematics'' *''Electronic Workshops in Computing ''Electronic Workshops in Computing'' (eWiC) is a publication series by the British Computer Society. The series provides free online access for conferences and workshops in the area of computing. For example, the EVA London Conference proceeding ...'', published by the British Computer Society References External links * Publications established in 1973 Computer science books Series of non-fiction books Springer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
STACS
The Symposium on Theoretical Aspects of Computer Science (STACS) is an academic conference in the field of computer science. It is held each year, alternately in Germany and France, since 1984. Typical themes of the conference include algorithms, computational and structural complexity, automata, formal languages and logic.STACS proceedings from 1984 to 2007have been published by Springer Science+Business Media in the Lecture Notes in Computer Science series. The proceedings since 2008 are published by the Leibniz Center for Informatics in the open access series Leibniz International Proceedings in Informatics. The proceedings since are freely available from the conference portal, as well as froDROPS the Dagstuhl Research Online Publication Server, and from Hyper Articles en Ligne. The conference is indexed by several bibliographic databases, including the DBLP, Google Scholar and The Collection of Computer Science Bibliographies. See also * The list of computer science confere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Chazelle
Bernard Chazelle (born November 5, 1955) is a French-American computer scientist. He is currently the Eugene Higgins Professor of Computer Science at Princeton University. Much of his work is in computational geometry, where he is known for his study of algorithms, such as linear-time triangulation of a simple polygon, as well as major complexity results, such as lower bound techniques based on discrepancy theory. He is also known for his invention of the soft heap data structure and the most asymptotically efficient known algorithm for finding minimum spanning trees. Early life Chazelle was born in Clamart, France, the son of Marie-Claire (née Blanc) and Jean Chazelle. He grew up in Paris, France, where he received his bachelor's degree and master's degree in applied mathematics at the École des mines de Paris in 1977. Then, at the age of 21, he attended Yale University in the United States, where he received his PhD in computer science in 1980 under the supervision of Da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangle Containing Points
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a ''square''. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Empty Circle
In computational geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in ''d''-dimensional space whose interior does not overlap with any given obstacles. Two dimensions The largest empty circle problem is the problem of finding a circle of largest radius in the plane whose interior does not overlap with any given obstacles. A common special case is as follows. Given ''n'' points in the plane, find a largest circle centered within their convex hull and enclosing none of them. The problem may be solved using Voronoi diagrams in optimal time \Theta(n\, \log\, n).Megan Schuster"The Largest Empty Circle Problem"/ref> See also *Bounding sphere *Farthest-first traversal *Largest empty rectangle In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
