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Geometric separator information


A geometric separator is a line (or another shape) that partitions a collection of geometric shapes into two subsets, such that proportion of shapes in each subset is bounded, and the number of shapes that do not belong to any subset (i.e. the shapes intersected by the separator itself) is small.

When a geometric separator exists, it can be used for building divide-and-conquer algorithms for solving various problems in computational geometry.

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Geometric separator

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A geometric separator is a line (or another shape) that partitions a collection of geometric shapes into two subsets, such that proportion of shapes in...

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Separator

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separator theorem, a theorem in graph theory Vertex separator, a notion in graph theory Geometric separator, a line that separates a set of geometric...

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Maximum disjoint set

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divide-and-conquer algorithms are based on a certain geometric separator theorem. A geometric separator is a line or shape that separates a given set of shapes...

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Aspect ratio

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Retrieved 18 February 2020. Smith, W. D.; Wormald, N. C. (1998). "Geometric separator theorems and applications". Proceedings 39th Annual Symposium on...

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Planar separator theorem

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In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split...

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Ham sandwich theorem

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1216/RMJ-1981-11-3-473, JSTOR 44236614. Smith, W. D.; Wormald, N. C. (1998), "Geometric separator theorems and applications", Proceedings 39th Annual Symposium on...

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Separation theorem

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n-dimensional Euclidean space. Also known as: Separating axis theorem. Geometric separator theorems - theorems regarding the existence of lines separating objects...

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Guillotine cutting

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a fraction 1/80 of the total weight can be separated. See also: Geometric separator Hyperplane separation theorem Some recently-studied variants of the...

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Shallow minor

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aspects of geometric graphs", Comput. Geom., 9 (4): 277–287, doi:10.1016/S0925-7721(96)00008-9, MR 1609578. Wulff-Nilsen, Christian (2011), "Separator Theorems...

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Helge Tverberg

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the Notices of the American Mathematical Society for April, 2011. Geometric separator Meet the mathematician, Helge Tverberg, University of Bergen, November...

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Whitespace character

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a sequence of whitespace characters is treated as a single inter-word separator, which may manifest as a single space character when rendering text in...

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Geometrical Product Specification and Verification

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Geometrical Product Specification and Verification (GPS&V) is a set of ISO standards developed by ISO Technical Committee 213. The aim of those standards...

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Universal Character Set characters

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baseline advance. Line Separator (U+2028) Paragraph Separator (U+2029) These provide Unicode with native paragraph and line separators independent of the...

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Topological graph

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topological graphs is the class of geometric graphs, where the edges are represented by line segments. (The term geometric graph is sometimes used in a broader...

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Numeral system

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1 corresponds to bijective numeration, where the zeros correspond to separators of numbers with digits which are non-zero. List of numeral systems Computer...

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Sanjeev Arora

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for 2012 for his work on improving the approximation ratio for graph separators and related problems from O ( log ⁡ n ) {\displaystyle O(\log n)} to O...

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Mathematical operators and symbols in Unicode

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U+239B–U+23B5, 23B7, U+23D0, and U+23DC–U+23E2. The Geometric Shapes block (U+25A0–U+25FF) contains geometric shape symbols. The math subset of this block is...

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De Laval nozzle

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the internal combustion engine Spacecraft propulsion Twister supersonic separator Isentropic nozzle flow Daniel Bernoulli Wikimedia Commons has media related...

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Equals sign

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of a double hyphen, the equal sign is sometimes used in Japanese as a separator between names. In Ojibwe, the readily available equal sign on a keyboard...

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Matroid

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is a separator that is neither E nor the empty set. An irreducible separator is a non-empty separator that contains no other non-empty separator. The...

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Glossary of mathematical symbols

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countries, may denote division. 3.  In set-builder notation, it is used as a separator meaning "such that"; see {□ : □}. /    (slash) 1.  Denotes division and...

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Isoperimetric inequality

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In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n {\displaystyle n} -dimensional...

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History of logarithms

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an integer power of 10. This can be envisioned as shifting the decimal separator of the given number to the left yielding a positive, and to the right...

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Nearest neighbor graph

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is a special case of the k-NNG, namely it is the 1-NNG. k-NNGs obey a separator theorem: they can be partitioned into two subgraphs of at most n(d + 1)/(d...

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List of theorems

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(plane geometry) Pizza theorem (geometry) Pivot theorem (circles) Planar separator theorem (graph theory) Plancherel theorem (Fourier analysis) Plancherel...

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