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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] |
Metric Geometry
In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a Conceptual metaphor , metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1-center Problem
The 1-center problem, also known as minimax problem or minmax location problem, is a classical combinatorial optimization problem in operations research of facilities location type. In its most general case the problem is stated as follows: given a set of ''n'' demand points, a space of feasible locations of a facility and a function to calculate the transportation cost between a facility and any demand point, find a location of the facility which minimizes the maximum facility-demand point transportation cost. There are numerous particular cases of the problem, depending on the choice of the locations both of demand points and facilities, as well as the distance function. A simple special case is when the feasible locations and demand points are in the plane with Euclidean distance as transportation cost (planar minmax Euclidean facility location problem, Euclidean 1-center problem in the plane, etc.). It is also known as the smallest circle problem. Its generalization to ''n''- ... [...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] |
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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SIAM Journal On Applied Mathematics
The ''SIAM Journal on Applied Mathematics'' is a peer-reviewed academic journal in applied mathematics published by the Society for Industrial and Applied Mathematics (SIAM), with Paul A. Martin (Colorado School of Mines) as its editor-in-chief. It was founded in 1953 as SIAM's first journal, the ''Journal of the Society for Industrial and Applied Mathematics'', and was given its current name in 1966. In most years since 1999, it has been ranked by SCImago Journal Rank as a second-quartile journal in applied mathematics. Together with ''Communications on Pure and Applied Mathematics ''Communications on Pure and Applied Mathematics'' is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences. It covers research originating from or solicited ...'' it has been called "one of the two greatest American entries in applied math".. References {{Society for Industrial and Applied Mathematics Applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Processing Letters
''Information Processing Letters'' is a peer review, peer-reviewed scientific journal in the field of computer science, published by Elsevier. The aim of the journal is to enable fast dissemination of results in the field of Data processing, information processing in the form of short papers. Submissions are limited to nine double-spaced pages. The scope of IPL covers fundamental aspects of information processing and computing. This naturally covers topics in the broadly understood field of theoretical computer science, including algorithms, formal languages and automata, computational complexity, computational logic, distributed and parallel algorithms, computational geometry, learning theory, computational number theory, computational biology, coding theory, theoretical cryptography, and applied discrete mathematics. Generally, submissions in all areas of scientific inquiry are considered, provided that they describe research contributions credibly motivated by applications to com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research (journal)
''Operations Research'' is a bimonthly peer-reviewed academic journal covering operations research that is published by the Institute for Operations Research and the Management Sciences. It was established in 1952 as the ''Journal of the Operations Research Society of America'' and obtained its current name in 1955. The editor-in-chief is Amy Ward (University of Chicago). Abstracting and indexing The journal is abstracted and indexed by ''Mathematical Reviews'', MathSciNet, Science Citation Index Expanded, Scopus, Social Sciences Citation Index, and ''Zentralblatt MATH''. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 2.604. References External links * Operations research journals Academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 |
Smallest-circle Problem
The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in ''n''-dimensional space, the smallest bounding sphere problem, is to compute the smallest ''n''-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857. The smallest-circle problem in the plane is an example of a facility location problem (the 1-center problem) in which the location of a new facility must be chosen to provide service to a number of customers, minimizing the farthest distance that any customer must travel to reach the new facility. Both the smallest circle problem in the plane, and the smallest bounding sphere problem in any hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Time
In theoretical 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 gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Sphere
In mathematics, given a non-empty set of objects of finite extension in d-dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is a d-dimensional solid sphere containing all of these objects. Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms with a high practical value in real-time computer graphics applications. In statistics and operations research, the objects are typically points, and generally the sphere of interest is the minimal bounding sphere, that is, the sphere with minimal radius among all bounding spheres. It may be proven that such a sphere is unique: If there are two of them, then the objects in question lie within their intersection. But an intersection of two non-coinciding spheres of equal radius is contained in a sphere of smaller radius. The problem of computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
