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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 ...
The problem was first proposed by Hakimi in 1964. [3]Let (,) be a metric space where is a set and is a metric A set , is provided together with a parameter .The goal is to find a subset with | | = such that the maximum distance of a point in to the closest point in is minimized.
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Lloyd's algorithm starts by an initial placement of some number k of point sites in the input domain. In mesh-smoothing applications, these would be the vertices of the mesh to be smoothed; in other applications they may be placed at random or by intersecting a uniform triangular mesh of the appropriate size with the input domain.
The unit distance graph for a set of points in the plane is the undirected graph having those points as its vertices, with an edge between two vertices whenever their Euclidean distance is exactly one. An abstract graph is said to be a unit distance graph if it is possible to find distinct locations in the plane for its vertices, so that its ...
GJK makes use of Johnson's distance sub algorithm, which computes in the general case the point of a tetrahedron closest to the origin, but is known to suffer from numerical robustness problems. In 2017 Montanari, Petrinic, and Barbieri proposed a new sub algorithm based on signed volumes which avoid the multiplication of potentially small ...
An approximate nearest neighbor search algorithm is allowed to return points whose distance from the query is at most times the distance from the query to its nearest points. The appeal of this approach is that, in many cases, an approximate nearest neighbor is almost as good as the exact one.