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X-tree
In computer science tree data structures, an X-tree (for ''eXtended node tree'') is an index tree structure based on the R-tree used for storing data in many dimensions. It appeared in 1996, and differs from R-trees (1984), R+-trees (1987) and R*-trees (1990) because it emphasizes prevention of overlap in the bounding boxes, which increasingly becomes a problem in high dimensions. In cases where nodes cannot be split without preventing overlap, the node split will be deferred, resulting in super-nodes. In extreme cases, the tree will linearize, which defends against worst-case behaviors observed in some other data structures. Structure The X-tree consists of three different types of nodes—data nodes, normal directory nodes and supernodes. The data nodes of the X-tree contain rectilinear minimum bounding rectangle In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R-tree
R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" (to display them in a navigation system) or "find the nearest gas station" (although not taking roads into account). The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance. R-tree idea The key idea of the data structure is to group nearby objects and represent the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (data Structure)
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent. These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R+-tree
An R+ tree is a method for looking up data using a location, often (x, y) coordinates, and often for locations on the surface of the earth. Searching on one number is a solved problem; searching on two or more, and asking for locations that are nearby in both x and y directions, requires craftier algorithms. Fundamentally, an R+ tree is a tree data structure, a variant of the R tree, used for indexing spatial information. Difference between R+ trees and R trees R+ trees are a compromise between R-tree R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found sign ...s and kd-trees: they avoid overlapping of internal nodes by inserting an object into multiple leaves if necessary. Coverage is the entire area to cover all related rectangles. Overlap is the entire area which is contained in two or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R*-tree
In data processing R*-trees are a variant of R-trees used for indexing spatial information. R*-trees have slightly higher construction cost than standard R-trees, as the data may need to be reinserted; but the resulting tree will usually have a better query performance. Like the standard R-tree, it can store both point and spatial data. It was proposed by Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, and Bernhard Seeger in 1990. Difference between R*-trees and R-trees Minimization of both coverage and overlap is crucial to the performance of R-trees. Overlap means that, on data query or insertion, more than one branch of the tree needs to be expanded (due to the way data is being split in regions which may overlap). A minimized coverage improves pruning performance, allowing exclusion of whole pages from search more often, in particular for negative range queries. The R*-tree attempts to reduce both, using a combination of a revised node split algorithm and the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Bounding Rectangle
In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its coordinate system; in other words , , , . The MBR is a 2-dimensional case of the minimum bounding box. MBRs are frequently used as an indication of the general position of a geographic feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes. The degree to which an "overlapping rectangles" query based on MBRs will be satisfactory (in other words, produce a low number of "false positive" hits) will depend on the extent to which individual spatial objects occupy (fill) their associated MBR. If the MBR is full or nearly so (for example, a mapsheet aligned with axes of latitude and longitude will normally entirely fill its associated MBR in the same coordinate space), then the "overlapping rectangles" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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