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| {{About|the data structure|the type of metric space|Real tree}}
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| A '''metric tree''' is any [[tree (data structure)|tree]] [[data structure]] specialized to index data in [[metric space]]s. Metric trees exploit properties of metric spaces such as the [[triangle inequality]] to make accesses to the data more efficient. Examples include the [[M-tree]], [[vp-tree]]s, [[cover tree]]s, [[MVP Tree]]s, and [[bk tree]]s.<ref name="Samet">{{cite book|last=Samet|first=Hanan|title=Foundations of multidimensional and metric data structures|year=2006|publisher=Morgan Kaufmann|isbn=978-0-12-369446-1|url=http://books.google.dk/books?id=KrQdmLjTSaQC}}</ref>
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| <!-- should have a list and summary of metric trees, with links to the main articles. -->
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| ==Multidimensional search==
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| Most algorithms and data structures for searching a dataset are based on the classical [[binary search]] algorithm, and generalizations such as the [[k-d tree]] or [[range tree]] work by interleaving the [[binary search algorithm]] over the separate coordinates and treating each spatial coordinate as an independent search constraint. These data structures are well-suited for [[range query]] problems asking for every point <math>(x,y)</math> that satisfies <math>\mbox{min}_x \leq x \leq \mbox{max}_x</math> and <math>\mbox{min}_y \leq y \leq \mbox{max}_y</math>.
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| A limitation of these multidimensional search structures is that they are only defined for searching over objects that can be treated as vectors. They aren't applicable for the more general case in which the algorithm is given only a collection of objects and a function for measuring the distance or similarity between two objects. If, for example, someone were to create a function that returns a value indicating how similar one image is to another, a natural algorithmic problem would be to take a dataset of images and find the ones that are similar according to the function to a given query image.
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| ==Metric data structures==
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| If there is no structure to the similarity measure then a [[brute force search]] requiring the comparison of the query image to every image in the dataset is the best that can be done. If, however, the similarity function satisfies the [[triangle inequality]] then it is possible to use the result of each comparison to prune the set of candidates to be examined.
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| The first article on metric trees, as well as the first use of the term "metric tree", published in the open literature was by [[Jeffrey Uhlmann]] in 1991.<ref>{{cite journal |last=Uhlmann |first=Jeffrey |title=Satisfying General Proximity/Similarity Queries with Metric Trees |journal=Information Processing Letters |volume=40 |number=4 |year=1991}}</ref> Other researchers were working independently on similar data structures. In particular, Peter Yianilos claimed to have independently discovered the same method, which he called a [[Vantage-point tree|vantage point tree]] (VP-tree).<ref name="pny93">{{cite conference
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| | first = Peter N.
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| | last = Yianilos
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| | authorlink =
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| | coauthors =
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| | title = Data structures and algorithms for nearest neighbor search in general metric spaces
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| | booktitle = Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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| | pages = 311–321
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| | publisher = Society for Industrial and Applied Mathematics Philadelphia, PA, USA
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| | year = 1993
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| | location =
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| | url = http://pnylab.com/pny/papers/vptree/vptree/
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| | accessdate = 2008-08-22
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| | id = pny93
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| }}</ref>
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| The research on metric tree data structures blossomed in the late 1990s and included an examination by Google co-founder [[Sergey Brin]] of their use for very large databases.<ref>{{cite conference |last=Brin |first=Sergey |title=Near Neighbor Search in Large Metric Spaces |booktitle=21st International Conference on Very Large Data Bases (VLDB) |year=1995}}</ref> The first textbook on metric data structures was published in 2006.<ref name="Samet"/>
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| ==References==
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| {{Reflist}}
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| {{CS-Trees}}
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| [[Category:Trees (data structures)]]
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Hi there, I am Andrew Berryhill. For many years she's been living in Kentucky but her spouse wants them to transfer. My working day job is an information officer but I've already applied for an additional 1. I am truly fond of handwriting but I can't make it my profession truly.
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