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The algorithm will always correctly determine the closest pair, because it maps any pair closer than distance to the same grid point or to adjacent grid points. The uniform sampling of pairs in the first step of the algorithm (compared to a different method of Rabin for sampling a similar number of pairs) simplifies the proof that the expected ...
Minimum bounding box algorithms: find the oriented minimum bounding box enclosing a set of points; Nearest neighbor search: find the nearest point or points to a query point; Nesting algorithm: make the most efficient use of material or space; Point in polygon algorithms: tests whether a given point lies within a given polygon
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 ...
The closest pair of points corresponds to two adjacent cells in the Voronoi diagram. If the setting is the Euclidean plane and a discrete set of points is given, then two points of the set are adjacent on the convex hull if and only if their Voronoi cells share an infinitely long side.
Closest pair problem: find the pair of points (from a set of points) with the smallest distance between them; Collision detection algorithms: check for the collision or intersection of two given solids; Cone algorithm: identify surface points; Convex hull algorithms: determining the convex hull of a set of points Graham scan; Quickhull
Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol. 3 of The Art of Computer Programming (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post ...
Closest pair of points problem, the algorithmic problem of finding two points that have the minimum distance among a larger set of points; Euclidean distance, the minimum length of any curve between two points in the plane; Shortest path problem, the minimum length of a path between two points in a graph
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects.. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, [1] although the term "closest point problem" is also used synonymously to the nearest neighbor search.