The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with the common part being that it is required to find the shortest interconnect for a given set of objects.
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Rectilinear Steiner tree
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plane, in which the Euclidean distance is replaced with the rectilinear distance. The problem may be formally stated as follows: given n points in the plane, it is required to interconnect them all by a shortest network which consists only of vertical and horizontal line segments.
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Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0,0).
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Point (geometry)
In geometry, topology, and related branches of mathematics, a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e. , they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics dealing with set theory, an element is sometimes referred to as a point.
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Approximation algorithm
In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions.
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Moment (mathematics)
In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a set of points. The "second moment", for example, is widely used and measures the "width" (in a particular sense) of a set of points in one dimension or in higher dimensions measures the shape of a cloud of points as it could be fit by an ellipsoid. Other moments describe other aspects of a distribution such as how the distribution is skewed from its mean, or peaked.
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Bracket
Brackets are tall punctuation marks used in matched pairs within text, to set apart or interject other text. Used unqualified, brackets refer to different types of brackets in different parts of the world and in different contexts.
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Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that areas above the axis add to the total, and the area below the x axis subtract from the total.
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