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Geometric Spanner
A geometric spanner or a -spanner graph or a -spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a -path between any pair of vertices for a fixed parameter . A -path is defined as a path through the graph with weight at most times the spatial distance between its endpoints. The parameter is called the stretch factor or dilation factor of the spanner. In computational geometry, the concept was first discussed by L.P. Chew in 1986, although the term "spanner" was not used in the original paper. The notion of graph spanners has been known in graph theory: -spanners are spanning subgraphs of graphs with similar dilation property, where distances between graph vertices are defined in graph-theoretical terms. Therefore geometric spanners are graph spanners of complete graphs embedded in the plane with edge weights equal to the distances between the embedded vertices in the corresponding metric. Spanners may be used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Weighted Graph
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I J K L M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
NP-hard
In computational complexity theory, a computational problem ''H'' is called NP-hard if, for every problem ''L'' which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from ''L'' to ''H''. That is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve a single NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time algorithms for NP-hard problems exist. A simple example of an NP-hard problem is the subset sum problem. Informally, if ''H'' is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
Journal Of The ACM
The ''Journal of the ACM'' (''JACM'') is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are i ...'' References External links * {{DEFAULTSORT:Journal Of The Acm Academic journals established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Well-separated Pair Decomposition
In computational geometry, a well-separated pair decomposition (WSPD) of a set of points S \subset \mathbb^d, is a sequence of pairs of sets (A_i, B_i), such that each pair is well-separated, and for each two distinct points p, q \in S, there exists precisely one pair which separates the two. The graph induced by a well-separated pair decomposition can serve as a k-spanner of the complete Euclidean graph, and is useful in approximating solutions to several problems pertaining to this. Definition Let A, B be two disjoint sets of points in \mathbb^d, R(X) denote the axis-aligned minimum bounding box for the points in X, and s > 0 denote the separation factor. We consider A and B to be well-separated, if for each of R(A) and R(B) there exists a d-ball of radius \rho containing it, such that the two spheres have a minimum distance of at least s \rho. We consider a sequence of well-separated pairs of subsets of S, (A_1, B_1), (A_2, B_2), \ldots, (A_m,B_m) to be a well-separate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 |
Delaunay Triangulation
In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles whose circumcircles do not contain any of the points; that is, each circumcircle has its generating points on its circumference, but all other points in the set are outside of it. This maximizes the size of the smallest angle in any of the triangles, and tends to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on it from 1934. If the points all lie on a straight line, the notion of triangulation becomes degenerate and there is no Delaunay triangulation. For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's ''Elements'', distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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Ingo Althöfer
Ingo Althöfer (born 1961) is a German mathematician and former professor of operations research at the University of Jena. Althöfer earned his PhD in 1986 at Bielefeld University. His dissertation, ''Asymptotic Properties of Certain Competition Systems in Artificial Intelligence and Ecology'', was supervised by Rudolf Ahlswede. Contributions Topics in Althöfer's professional research include the realization of finite metric spaces by shortest path metrics in graphs and their approximation by greedy spanners, algorithmic game theory and combinatorial game theory, and heuristic search algorithms for optimization problems. Althöfer is also known for his inventions of games and puzzles, including dice game EinStein würfelt nicht!, for his experiments with self-assembly of Lego building blocks by running them through a washing machine, and for his innovations in computer-human chess playing. In the 1990s he tested his "drei hirn" 3-brains"system, in which a human decides b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gautam Das (computer Scientist)
Gautam Das is a computer scientist in the field of databases research. He is an ACM Fellow (since 2021) and IEEE Fellow (since 2020). He is a Distinguished University Chair Professor of Computer Science and Engineering, Associate Dean of Research of College of Engineering at the University of Texas at Arlington, and director of the Database Exploration Laboratory (DBXLAB) at the CSE department at UTA. His is known for his work in databases, data mining, computational geometry, and algorithms. Biography He graduated with a B.Tech. in computer science from IIT Kanpur, India, and with a Ph.D. in computer science from the University of Wisconsin, Madison. Prior to joining UTA in 2004, Das has held positions at Microsoft Research, Compaq and the University of Memphis. Research Das's early research interests were in computational geometry and graph algorithms. His Ph.D. dissertation made several significant contributions, most notably the discovery of greedy graph spanners. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
