The closest pair of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find...

registration Computational geometry – see Closest pair of points problem Cryptanalysis – for lattice problem Databases – e.g. content-based image retrieval...

problems stated in terms of points only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously...

applied.[how?] Mathematics portal Nearest centroid classifier Closest pair of points problem Nearest neighbor graph Segmentation-based object categorization...

that is tangent to the circle and has the given points as its foci. Although special cases of this problem were studied by Ptolemy in the 2nd century CE...

related to the complexity of computing bichromatic closest pairs. In the bichromatic closest pair problem, the input is a set of points, given two different...

each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in...

A kinetic closest pair data structure is a kinetic data structure that maintains the closest pair of points, given a set P of n points that are moving...

set of edges that connect points of the plane, the problem to determine whether they contain a triangulation is NP-complete. Some triangulations of a set...

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...

data Closest pair of points problem, the algorithmic problem of finding two points that have the minimum distance among a larger set of points Euclidean...

as problems at all until the advent of computers. Consider, for example, the closest pair problem: Given n points in the plane, find the two with the...

relationship as a pair of intersecting circles". Its solution involves a transcendental equation. The problem derives from "A Country House Visit", one of Jan Struther's...

devoted to solving problems of a geometric nature. This field includes problems from classic geometry, like the closest pair of points problem, as well as more...

problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944. A line that contains exactly two of a set of points...

well-separated pair decomposition (WSPD) of a set of points S ⊂ R d {\displaystyle S\subset \mathbb {R} ^{d}} , is a sequence of pairs of sets ( A i , B...

problem in mathematics What is the asymptotic growth rate of the area of the smallest triangle determined by three out of n {\displaystyle n} points in...

point to the cluster with the closest centroid.[citation needed] Using only the centroid to redistribute the data has problems when clusters lack uniform...

as an instance of the closest pair of points problem, taking worst-case time O(n log n) or (with randomized time and with the use of the floor function)...

many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points...

computer science, the maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest...

1988: Closest pair". In Aggarwal, Alok; Wein, Joel (eds.). Computational Geometry: Lecture Notes for 18.409, Spring 1988. Massachusetts Institute of Technology...

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal...

calculus operation of indefinite integration (i.e. finding antiderivatives) Closest pair problem: find the pair of points (from a set of points) with the smallest...

In this way, it avoids the problem of repeatedly finding closest pairs. Nevertheless, for many types of clustering problem, it can be guaranteed to come...

of triangular numbers are connected to theta functions, in particular the Ramanujan theta function. The number of line segments between closest pairs...

be confused with ray tracing of computer graphics) Slab method Closest pair of points Closest point problem Diameter of a point set Delaunay triangulation...

addresses one of DBSCAN's major weaknesses: the problem of detecting meaningful clusters in data of varying density. To do so, the points of the database...

be a pair in this intermediate range has been observed in PKS 1302-102. The question of how this happens is the "final parsec problem". A number of solutions...

excessive number of nodes, bending and stretching. Then the so-called "metro map" is constructed. The data points are projected into the closest node. For each...