The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane[1] was among the first geometric problems that were treated at the origins of the systematic study of the computational complexity of geometric algorithms.
^Shamos, Michael Ian; Hoey, Dan (1975). "Closest-point problems". 16th Annual Symposium on Foundations of Computer Science, Berkeley, California, USA, October 13-15, 1975. IEEE Computer Society. pp. 151–162. doi:10.1109/SFCS.1975.8.
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registration Computational geometry – see Closestpairofpointsproblem Cryptanalysis – for lattice problem Databases – e.g. content-based image retrieval...
problems stated in terms ofpoints only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously...
related to the complexity of computing bichromatic closestpairs. In the bichromatic closestpairproblem, the input is a set ofpoints, given two different...
each pairof 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...
devoted to solving problemsof a geometric nature. This field includes problems from classic geometry, like the closestpairofpointsproblem, as well as more...
point to the cluster with the closest centroid.[citation needed] Using only the centroid to redistribute the data has problems when clusters lack uniform...
1988: Closestpair". In Aggarwal, Alok; Wein, Joel (eds.). Computational Geometry: Lecture Notes for 18.409, Spring 1988. Massachusetts Institute of Technology...
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...
is a set ofpoints Ai which have M as median in all directions, but for which the points not coincident with M do not come in balanced pairs. Then we...
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...
be confused with ray tracing of computer graphics) Slab method ClosestpairofpointsClosest point problem Diameter of a point set Delaunay triangulation...
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...
addresses one of DBSCAN's major weaknesses: the problemof detecting meaningful clusters in data of varying density. To do so, the pointsof the database...
calculus operation of indefinite integration (i.e. finding antiderivatives) Closestpairproblem: find the pairofpoints (from a set ofpoints) with the smallest...
as an instance of the closestpairofpointsproblem, taking worst-case time O(n log n) or (with randomized time and with the use of the floor function)...
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