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Diameter (computational Geometry)
In computational geometry, the diameter of a finite set of points or of a polygon is its diameter as a set, the largest distance between any two points. The diameter is always attained by two points of the convex hull of the input. A trivial brute-force search can be used to find the diameter of n points in time O(n^2) (assuming constant-time distance evaluations) but faster algorithms are possible for points in low dimensions. Static 2d input In two dimensions, the diameter can be obtained by computing the convex hull and then applying the method of rotating calipers. This involves finding two parallel support lines for the convex hull (for instance vertical lines through the two vertices with minimum and maximum x-coordinate) and then rotating the two lines through a sequence of discrete steps that keep them as parallel lines of support until they have rotated back to their original orientation. The diameter is the maximum distance between any pair of convex hull vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ε-net (computational Geometry)
In computational geometry, an ''ε''-net (pronounced epsilon-net) is the approximation of a general set by a collection of simpler subsets. In probability theory it is the approximation of one probability distribution by another. Background Let ''X'' be a set and R be a set of subsets of ''X''; such a pair is called a ''range space'' or hypergraph, and the elements of ''R'' are called ''ranges'' or ''hyperedges''. An ε-net of a subset ''P'' of ''X'' is a subset ''N'' of ''P'' such that any range ''r'' ∈ R with , ''r'' ∩ ''P'', ≥ ''ε'', ''P'', intersects ''N''.. In other words, any range that intersects at least a proportion ε of the elements of ''P'' must also intersect the ''ε''-net ''N''. For example, suppose ''X'' is the set of points in the two-dimensional plane, ''R'' is the set of closed filled rectangles (products of closed intervals), and ''P'' is the unit square , 1nbsp;× , 1 Then the set N consis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 |
International Journal Of Computational Geometry & Applications
The ''International Journal of Computational Geometry and Applications'' (IJCGA) is a bimonthly journal published since 1991, by World Scientific. It covers the application of computational geometry in design and analysis of algorithms, focusing on problems arising in various fields of science and engineering such as computer-aided geometry design (CAGD), operations research, and others. The current editors-in-chief are D.-T. Lee of the Institute of Information Science in Taiwan, and Joseph S. B. Mitchell from the Department of Applied Mathematics and Statistics in the State University of New York at Stony Brook. Abstracting and indexing * Current Contents/Engineering, Computing & Technology * ISI Alerting Services * Science Citation Index Expanded (also known as SciSearch) * CompuMath Citation Index * Mathematical Reviews * INSPEC * DBLP Bibliography Server * Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmica
''Algorithmica'' is a monthly peer-reviewed scientific journal focusing on research and the application of computer science algorithms. The journal was established in 1986 and is published by Springer Science+Business Media. The editor in chief is Mohammad Hajiaghayi. Subject coverage includes sorting, searching, data structures, computational geometry, and linear programming, VLSI, distributed computing, parallel processing, computer aided design, robotics, graphics, data base design, and software tool A programming tool or software development tool is a computer program that is used to software development, develop another computer program, usually by helping the developer manage computer files. For example, a programmer may use a tool called ...s. Springer Science+Business Media. 2013 Abstract ...
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Computational Geometry (journal)
''Computational Geometry'', also known as ''Computational Geometry: Theory and Applications'', is a peer-reviewed mathematics journal for research in theoretical and applied computational geometry, its applications, techniques, and design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects, as well as fundamental problems in various areas of application of computational geometry: in computer graphics, pattern recognition, image processing, robotics, electronic design automation, CAD/CAM, and geographical information systems. The journal was founded in 1991 by Jörg-Rüdiger Sack and Jorge Urrutia.. It is indexed by ''Mathematical Reviews'', Zentralblatt MATH, Science Citation Index, and Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate, formerly the Institute for Scientific Information and Thomson Reuters. It is published online ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * '' Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate, formerly the Institute for Scientific Information and Thomson Reuters. It is published online and in several different printed subject sections. History ''Current Contents ...'' Notable articles Two articles published in ''Discrete & Computational Geometry'', one by Gil Kalai in 1992 with a proof of a subexponential upper bound on the diameter of a polytope and another by Samuel Ferguson in 2006 on the Kepler conjecture on optimal three-dimensional sphere packing, earned their authors the Fulk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Journal Of Computational Geometry And Applications
The ''International Journal of Computational Geometry and Applications'' (IJCGA) is a bimonthly journal published since 1991, by World Scientific. It covers the application of computational geometry in design and analysis of algorithms, focusing on problems arising in various fields of science and engineering such as computer-aided geometry design (CAGD), operations research, and others. The current editors-in-chief are D.-T. Lee of the Institute of Information Science in Taiwan, and Joseph S. B. Mitchell from the Department of Applied Mathematics and Statistics in the State University of New York at Stony Brook. Abstracting and indexing * Current Contents/Engineering, Computing & Technology * ISI Alerting Services * Science Citation Index Expanded (also known as SciSearch) * CompuMath Citation Index * Mathematical Reviews * INSPEC * DBLP Bibliography Server * Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanning Tree
In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself). Applications Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The Intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diameter (graph Theory)
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of a set for the set of vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs. Researchers have studied the problem of computing the diameter, both in arbitrary graphs and in special classes of graphs. The diameter of a disconnected graph may be defined to be infinite, or undefined. Graphs of low diameter The degree diameter problem seeks tight relations between the diameter, number of vertices, and degree of a graph. One way of formulating it is to ask for the largest graph with given bounds on its degree and diameter. For any fixed degree, this maximum size is exponential in diameter, with the base of the exponent depending on the degree. The girth of a graph, the length of its shortest cycle, can be at most 2k+1 for a graph of diameter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum-diameter Spanning Tree
In metric geometry and computational geometry, a minimum-diameter spanning tree of a finite set of points in a metric space is a spanning tree in which the diameter (the longest path length in the tree between two of its points) is as small as possible. In general metric spaces It is always possible to find a minimum-diameter spanning tree with one or two vertices that are not leaves. This can be proven by transforming any other tree into a tree of this special form, without increasing its diameter. To do so, consider the longest path in any given tree (its diameter path), and the vertex or edge at the midpoint of this path. If there is a vertex at the midpoint, it is the non-leaf vertex of a star, whose diameter is at most that of the given tree. If the midpoint is interior to an edge of the given tree, then there exists a tree that includes this edge, and in which every remaining vertex is a leaf connected to the endpoint of this edge that is nearest in the given tree, with di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Diameter (data)
A kinetic diameter data structure is a kinetic data structure which maintains the diameter of a set of moving points. The diameter of a set of moving points is the maximum distance between any pair of points in the set. In the two dimensional case, the kinetic data structure for kinetic convex hull can be used to construct a kinetic data structure for the diameter of a moving point set that is responsive, compact and efficient. 2D Case The pair of points with maximum pairwise distance must be one of the pairs of antipodal points of the convex hull of all of the points. Note that two points are antipodal points if they have parallel supporting lines. In the static case, the diameter of a point set can be found by computing the convex hull of the point set, finding all pairs of antipodal points, and then finding the maximum distance between these pairs. This algorithm can be kinetized as follows: Consider the dual of the point set. The points dualize to lines and the convex hull ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
