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Kirkpatrick–Seidel algorithm

Index Kirkpatrick–Seidel algorithm

The Kirkpatrick–Seidel algorithm, called by its authors "the ultimate planar convex hull algorithm", is an algorithm for computing the convex hull of a set of points in the plane, with \mathcal(n \log h) time complexity, where n is the number of input points and h is the number of points (non dominated or maximal points, as called in some texts) in the hull. [1]

14 relations: Algorithm, Analysis of algorithms, Bitangent, Convex hull, Convex hull algorithms, David G. Kirkpatrick, Divide and conquer algorithm, Franco P. Preparata, Gift wrapping algorithm, Median, Output-sensitive algorithm, Raimund Seidel, Recursion, SIAM Journal on Computing.

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Analysis of algorithms

In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them.

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Bitangent

In mathematics, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction as C at these points.

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Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Convex hull algorithms

Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science.

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David G. Kirkpatrick

David Galer Kirkpatrick is a Professor Emeritus of computer science at the University of British Columbia.

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Divide and conquer algorithm

In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion.

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Franco P. Preparata

Franco P. Preparata is a computer scientist, the An Wang Professor, Emeritus, of Computer Science at Brown University.

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Gift wrapping algorithm

In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.

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Median

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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Output-sensitive algorithm

In computer science, an output-sensitive algorithm is an algorithm whose running time depends on the size of the output, instead of, or in addition to, the size of the input.

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Raimund Seidel

Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry.

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Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

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SIAM Journal on Computing

The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science.

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Kirkpatrick-Seidel algorithm, Ultimate convex hull algorithm, Ultimate planar convex hull algorithm.

References

[1] https://en.wikipedia.org/wiki/Kirkpatrick–Seidel_algorithm

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