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M-tree
In computer science, M-trees are tree data structures that are similar to R-trees and B-trees. It is constructed using a metric and relies on the triangle inequality for efficient range and k-nearest neighbor (k-NN) queries. While M-trees can perform well in many conditions, the tree can also have large overlap and there is no clear strategy on how to best avoid overlap. In addition, it can only be used for distance functions that satisfy the triangle inequality, while many advanced dissimilarity functions used in information retrieval do not satisfy this. Overview As in any tree-based data structure, the M-tree is composed of nodes and leaves. In each node there is a data object that identifies it uniquely and a pointer to a sub-tree where its children reside. Every leaf has several data objects. For each node there is a radius r that defines a Ball in the desired metric space. Thus, every node n and leaf l residing in a particular node N is at most distance r from N, and e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Index
A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spatial databases allow the representation of simple geometric objects such as points, lines and polygons. Some spatial databases handle more complex structures such as 3D objects, topological coverages, linear networks, and triangulated irregular networks (TINs). While typical databases have developed to manage various numeric and character types of data, such databases require additional functionality to process spatial data types efficiently, and developers have often added ''geometry'' or ''feature'' data types. Geographic database (or geodatabase) is a georeferenced spatial database, used for storing and manipulating geographic data (or geodata, i.e., data associated with a location on Earth), especially in geographic infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Segment Tree
In computer science, the segment tree is a data structure used for storing information about Interval (mathematics), intervals or segments. It allows querying which of the stored segments contain a given point. A similar data structure is the interval tree. A segment tree for a set of ''n'' intervals uses Big O notation, ''O''(''n'' log ''n'') storage and can be built in ''O''(''n'' log ''n'') time. Segment trees support searching for all the intervals that contain a query point in time ''O''(log ''n'' + ''k''), ''k'' being the number of retrieved intervals or segments. Applications of the segment tree are in the areas of computational geometry, geographic information systems and machine learning. The segment tree can be generalized to higher dimension spaces. Definition Description Let be a set of intervals, or segments. Let ''p''1, ''p''2, ..., ''pm'' be the list of distinct interval endpoints, sorted from left to right. Consider the partitioning of the real line induced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trees (data Structures)
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cover Tree
The cover tree is a type of data structure in computer science that is specifically designed to facilitate the speed-up of a nearest neighbor search. It is a refinement of the Navigating Net data structure, and related to a variety of other data structures developed for indexing intrinsically low-dimensional data.Kenneth Clarkson. Nearest-neighbor searching and metric space dimensions. In G. Shakhnarovich, T. Darrell, and P. Indyk, editors, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, pages 15--59. MIT Press, 2006. The tree can be thought of as a hierarchy of levels with the top level containing the root point and the bottom level containing every point in the metric space. Each level ''C'' is associated with an integer value ''i'' that decrements by one as the tree is descended. Each level ''C'' in the cover tree has three important properties: *Nesting: C_ \subseteq C_ *Covering: For every point p \in C_, there exists a point q \in C_ such that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GiST
In computing, GiST or Generalized Search Tree, is a data structure and API that can be used to build a variety of disk-based search trees. GiST is a generalization of the B+ tree, providing a concurrent and recoverable height-balanced search tree infrastructure without making any assumptions about the type of data being stored, or the queries being serviced. GiST can be used to easily implement a range of well-known indexes, including B+ trees, R-trees, hB-trees, RD-trees, and many others; it also allows for easy development of specialized indexes for new data types. It cannot be used directly to implement non-height-balanced trees such as quad trees or prefix trees (tries), though like prefix trees it does support compression, including lossy compression. GiST can be used for any data type that can be naturally ordered into a hierarchy of supersets. Not only is it extensible in terms of data type support and tree layout, it allows the extension writer to support any query pred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Volume Hierarchy
A bounding volume hierarchy (BVH) is a tree structure on a set of geometric objects. All geometric objects, which form the leaf nodes of the tree, are wrapped in bounding volumes. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are also grouped and enclosed within other larger bounding volumes in a recursive fashion, eventually resulting in a tree structure with a single bounding volume at the top of the tree. Bounding volume hierarchies are used to support several operations on sets of geometric objects efficiently, such as in collision detection and ray tracing (graphics), ray tracing. Although wrapping objects in bounding volumes and performing collision tests on them before testing the object geometry itself simplifies the tests and can result in significant performance improvements, the same number of pairwise tests between bounding volumes are still being performed. By arranging the bounding volumes into a bounding volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Tree
In computer science, an interval tree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries, for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the segment tree. The trivial solution is to visit each interval and test whether it intersects the given point or interval, which requires O(n) time, where n is the number of intervals in the collection. Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is asymptotically optimal; however, we can do better by considering output-sensitive algorithms, where the runtime is expressed in terms of m, the number of intervals produced by the query. Interval trees have a query time of O(\log n + m) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
