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- Fixed-radius_near_neighbors abstract "In computational geometry, the fixed-radius near neighbor problem is a variant of the nearest neighbor search problem. In the fixed-radius near neighbor problem, one is given as input a set of points in d-dimensional Euclidean space and a fixed distance Δ. One must design a data structure that, given a query point q, efficiently reports the points of the data structure that are within distance Δ of q. The problem has long been studied; Bentley (1975) cites a 1966 paper by Levinthal that uses this technique as part of a system for visualizing molecular structures, and it has many other applications.One method for solving the problem is to round the points to an integer lattice, scaled so that the distance between grid points is the desired distance Δ. A hash table can be used to find, for each input point, the other inputs that are mapped to nearby grid points, which can then be tested for whether their unrounded positions are actually within distance Δ. The number of pairs of points tested by this procedure, and the time for the procedure, is linear in the combined input and output size when the dimension is a fixed constant. However, the constant of proportionality in the linear time bound grows exponentially as a function of the dimension. Using this method, it is possible to construct indifference graphs and unit disk graphs from geometric data in linear time.The fixed-radius near neighbors problem arises in continuous Lagrangian simulations (such as smoothed particle hydrodynamics), computational geometry, and point cloud problems (surface reconstructions). Modern parallel methods for GPU are able to efficiently compute all pairs fixed-radius NNS. For finite domains, the method of Green shows the problem can be solved by sorting on a uniform grid, finding all neighbors of all particles in O(kn) time, where k is proportional to the average number of neighbors. Hoetzlein improves this further on modern hardware with counting sorting and atomic operations.".
- Fixed-radius_near_neighbors wikiPageID "22504754".
- Fixed-radius_near_neighbors wikiPageLength "3388".
- Fixed-radius_near_neighbors wikiPageOutDegree "10".
- Fixed-radius_near_neighbors wikiPageRevisionID "617150798".
- Fixed-radius_near_neighbors wikiPageWikiLink Category:Geometric_algorithms.
- Fixed-radius_near_neighbors wikiPageWikiLink Computational_geometry.
- Fixed-radius_near_neighbors wikiPageWikiLink Constant_of_proportionality.
- Fixed-radius_near_neighbors wikiPageWikiLink Euclidean_space.
- Fixed-radius_near_neighbors wikiPageWikiLink Exponential_growth.
- Fixed-radius_near_neighbors wikiPageWikiLink Hash_table.
- Fixed-radius_near_neighbors wikiPageWikiLink Indifference_graph.
- Fixed-radius_near_neighbors wikiPageWikiLink Integer_lattice.
- Fixed-radius_near_neighbors wikiPageWikiLink Nearest_neighbor_search.
- Fixed-radius_near_neighbors wikiPageWikiLink Proportionality_(mathematics).
- Fixed-radius_near_neighbors wikiPageWikiLink Unit_disk_graph.
- Fixed-radius_near_neighbors wikiPageWikiLinkText "-neighborhood query".
- Fixed-radius_near_neighbors wikiPageWikiLinkText "Fixed-radius near neighbors".
- Fixed-radius_near_neighbors wikiPageWikiLinkText "fixed-radius near neighbors".
- Fixed-radius_near_neighbors wikiPageWikiLinkText "nearby neighbors".
- Fixed-radius_near_neighbors wikiPageWikiLinkText "neighborhood query".
- Fixed-radius_near_neighbors hasPhotoCollection Fixed-radius_near_neighbors.
- Fixed-radius_near_neighbors wikiPageUsesTemplate Template:Geometry-stub.
- Fixed-radius_near_neighbors wikiPageUsesTemplate Template:Harvtxt.
- Fixed-radius_near_neighbors wikiPageUsesTemplate Template:Reflist.
- Fixed-radius_near_neighbors subject Category:Geometric_algorithms.
- Fixed-radius_near_neighbors hypernym Variant.
- Fixed-radius_near_neighbors type Algorithm.
- Fixed-radius_near_neighbors comment "In computational geometry, the fixed-radius near neighbor problem is a variant of the nearest neighbor search problem. In the fixed-radius near neighbor problem, one is given as input a set of points in d-dimensional Euclidean space and a fixed distance Δ. One must design a data structure that, given a query point q, efficiently reports the points of the data structure that are within distance Δ of q.".
- Fixed-radius_near_neighbors label "Fixed-radius near neighbors".
- Fixed-radius_near_neighbors sameAs m.05zzrnl.
- Fixed-radius_near_neighbors sameAs Q5456333.
- Fixed-radius_near_neighbors sameAs Q5456333.
- Fixed-radius_near_neighbors wasDerivedFrom Fixed-radius_near_neighbors?oldid=617150798.
- Fixed-radius_near_neighbors isPrimaryTopicOf Fixed-radius_near_neighbors.