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| {{Context|date=June 2010}}
| | There are many online companies that write custom scholarship essays for students. Term Paper Help As we have discussed before that, if you need any sort of help regarding term paper help, so you can any time contact with us and we will tackle your problems. This is a thought or hypothesis that you will either support or refute in your essay. You need to learn to avoid mistakes and focus more on quality. There is a strong possibility that two students of the same class have bought the same essay. <br><br>There are three major elements of deductive essays that one should consider while writing deductive essays. However, there are essay writing companies which can help these students survive college. Contrary to early reports from the Washington POST, the SAT essay is not dead yet. Every good essay begins with a thought or argument called 'a thesis. They should be followed and tweaked so that you are producing the quality content your readers deserve. <br><br>Think about how you are going to complete the task whilst simultaneously maximising the available marks in each section. com will provide a very good opportunity for college students to get involved in a greater capacity in writing their essays. Narrate the whole story through writing in a way that can be easily understood by the reader. Think about how this reflects ideas in the poem, for example a very uneven structure could represent ideas of chaos or lack of control. A student always wants a unique and well-structured piece of composition so that he or she can present it confidently in front of the tutors and get high scores. <br><br>This way will assist as it is so complicated to detect mistakes in your work. There is customer care team that is available to the customers at any hour of the day. Likewise to the similarities, the next part of writing a compare and contrast essay is to find out the differences among them. In the Academy of Art New Delhi the students have the opportunities to get the educational degrees in Interior designing, retail designing and visual merchandising. This is important to ensure that you buy essay papers that are right, appropriate, and of high quality. <br><br>If you have any kind of questions relating to in which and also the way to use [http://www.playbestpuzzlegames.com/profile/phkemble do my homework], you are able to email us with the web site. Write a quick schedule to help you allocate your time wisely: list the days you have left and the time during the day you will be able to work. should always be the principal priority of a company. You may have problems in understanding the subjects. Our essay writing website is the best original essay writing service one can come across while searching for original papers, original essays, original term papers, original research papers, original academic papers, original thesis papers or original English essay writing. You should conclude the essay by focusing on the main purpose of the essay. |
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| '''M-trees''' are [[tree data structure]]s that are similar to [[R-tree]]s and [[B-tree]]s. It is constructed using a [[Metric (mathematics)|metric]] and relies on the [[triangle inequality]] for efficient range and [[k-nearest neighbor algorithm|k-NN]] queries.
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| 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 function]]s that satisfy the triangle inequality, while many advanced dissimilarity functions used in [[information retrieval]] do not satisfy this.<ref name="p426">{{cite conference
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| | first = Paolo
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| | last = Ciaccia
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| | authorlink =
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| | coauthors = Patella, Marco; Zezula, Pavel
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| | title = M-tree An Efficient Access Method for Similarity Search in Metric Spaces
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| | booktitle = Proceedings of the 23rd VLDB Conference Athens, Greece, 1997
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| | pages = 426–435
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| | publisher = Very Large Databases Endowment Inc.
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| | year = 1997
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| | location = IBM Almaden Research Center
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| | url = http://www.vldb.org/conf/1997/P426.PDF
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| | accessdate = 2010-09-07
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| | id = p426
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| }}</ref>
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| ==Overview==
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| [[File:Mtree-2d.svg|thumb|350px|2D M-Tree visualized using [[Environment for DeveLoping KDD-Applications Supported by Index-Structures|ELKI]]. The tree has a single level of leaf nodes. Due to a suboptimal split heuristic, there is a large overlap.]]
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| 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 <math>n</math> and leaf <math>l</math> residing in a particular node <math>N</math> is at most distance <math>r</math> from <math>N</math>, and every node ''n'' and leaf ''l'' with node parent ''N'' keep the distance from it.
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| ==M-Tree construction==
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| === Components ===
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| An M-Tree has these components and sub-components:
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| # Non-leaf nodes
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| ## A set of routing objects N<sub>''RO''</sub>.
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| ## Pointer to Node's parent object O<sub>''p''</sub>.
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| # Leaf nodes
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| ## A set of objects N<sub>''O''</sub>.
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| ## Pointer to Node's parent object O<sub>''p''</sub>.
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| # Routing Object
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| ## (Feature value of) routing object O<sub>''r''</sub>.
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| ## Covering radius r(O<sub>''r''</sub>).
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| ## Pointer to covering tree T(O<sub>''r''</sub>).
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| ## Distance of O<sub>''r''</sub> from its parent object d(O<sub>''r''</sub>,P(O<sub>''r''</sub>))
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| # Object
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| ## (Feature value of the) object O<sub>''j''</sub>.
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| ## Object identifier oid(O<sub>''j''</sub>).
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| ## Distance of O<sub>''j''</sub> from its parent object d(O<sub>''j''</sub>,P(O<sub>''j''</sub>))
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| === Insert ===
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| The main idea is first to find a leaf node <math>N</math> where the new object <math>O</math> belongs. If <math>N</math> is not full then just attach it to <math>N</math>. If <math>N</math> is full then invoke a method to split <math>N</math>. The algorithm is as follows:
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| {{algorithm-begin|name=Insert}}
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| Input: Node <math>N</math> of M-Tree <math>MT</math>, Entry <math>O_{n}</math>
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| Output: A new instance of <math>MT</math> containing all entries in original <math>MT</math> plus <math>O_{n}</math>
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| <math>N_{e}</math> ← <math>N</math>'s routing objects or objects
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| '''if''' <math>N</math> is not a leaf '''then'''
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| {
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| /*Look for entries that the new object fits into*/
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| let <math>N_{in}</math> be routing objects from <math>N_{e}</math>'s set of routing objects <math>N_{RO}</math> such that <math>d(O_{r}, O_{n}) <= r(O_{r})</math>
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| '''if''' <math>N_{in}</math> is not empty '''then'''
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| {
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| /*If there are one or more entry, then look for an entry such that is closer to the new object*/
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| <math>O_{r}^{*} = \min_{O_{r}\in N_{in}} d(O_{r}, O_{n})</math>
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| }
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| '''else'''
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| {
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| /*If there are no such entry, then look for an object with minimal distance from */
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| /*its covering radius's edge to the new object*/
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| <math>O_{r}^{*} = \min_{O_{r}\in N_{in}} d(O_{r}, O_{n}) - r(O_{r})</math>
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| /*Upgrade the new radii of the entry*/
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| <math>r(O_{r}^{*})</math> = <math>d(O_{r}^{*}, O_{n})</math>
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| }
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| /*Continue inserting in the next level*/
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| return insert(<math>T(O_{r}^{*})</math>, <math>O_{n}</math>);
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| '''else'''
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| {
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| /*If the node has capacity then just insert the new object*/
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| '''if''' <math>N</math> is not full '''then'''
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| { store(<math>N</math>, <math>O_{n}</math>) }
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| /*The node is at full capacity, then it is needed to do a new split in this level*/
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| '''else'''
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| { split(<math>N</math>, <math>O_{n}</math>) }
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| }
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| {{algorithm-end}}
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| === Split ===
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| If the split method arrives to the root of the tree, then it choose two routing objects from <math>N</math>, and creates two new nodes containing all the objects in original <math>N</math>, and store them into the new root. If split methods arrives to a node <math>N</math> that is not the root of the tree, the method choose two new routing objects from <math>N</math>, re-arrange every routing object in <math>N</math> in two new nodes <math>N_{1}</math> and <math>N_{2}</math>, and store this new nodes in the parent node <math>N_{p}</math> of original <math>N</math>. The split must be repeated if <math>N_{p}</math> has not enough capacity to store <math>N_{2}</math>. The algorithm is as follow:
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| {{algorithm-begin|name=Split}}
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| Input: Node <math>N</math> of M-Tree <math>MT</math>, Entry <math>O_{n}</math>
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| Output: A new instance of <math>MT</math> containing a new partition.
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| /*The new routing objects are now all those in the node plus the new routing object*/
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| let be <math>NN</math> entries of <math>N \cup O</math>
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| '''if''' <math>N</math> is not the root '''then'''
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| {
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| /*Get the parent node and the parent routing object*/
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| let <math>O_{p}</math> be the parent routing object of <math>N</math>
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| let <math>N_{p}</math> be the parent node of <math>N</math>
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| }
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| /*This node will contain part of the objects of the node to be split*/
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| Create a new node <math>N'</math>
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| /*Promote two routing objects from the node to be split, to be new routing objects*/
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| Create new objects <math>O_{p1}</math> and <math>O_{p2}</math>.
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| Promote(<math>N</math>, <math>O_{p1}</math>, <math>O_{p2}</math>)
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| /*Choose which objects from the node being split will act as new routing objects*/
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| Partition(<math>N</math>, <math>O_{p1}</math>, <math>O_{p2}</math>, <math>N_{1}</math>, <math>N_{2}</math>)
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| /*Store entries in each new routing object*/
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| Store <math>N_{1}</math>'s entries in <math>N</math> and <math>N_{2}</math>'s entries in <math>N'</math>
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| '''if''' <math>N</math> is the current root '''then'''
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| {
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| /*Create a new node and set it as new root and store the new routing objects*/
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| Create a new root node <math>N_{p}</math>
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| Store <math>O_{p1}</math> and <math>O_{p2}</math> in <math>N_{p}</math>
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| }
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| '''else'''
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| {
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| /*Now use the parent rouing object to store one of the new objects*/
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| Replace entry <math>O_{p}</math> with entry <math>O_{p1}</math> in <math>N_{p}</math>
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| '''if''' <math>N_{p}</math> is no full '''then'''
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| {
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| /*The second routinb object is stored in the parent only if it has free capacity*/
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| Store <math>O_{p2}</math> in <math>N_{p}</math>
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| }
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| '''else'''
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| {
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| /*If there is no free capacity then split the level up*/
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| split(<math>N_{p}</math>, <math>O_{p2}</math>)
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| }
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| }
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| {{algorithm-end}}
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| | |
| == M-Tree Queries ==
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| === Range Query ===
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| A range query is where a minimum similarity/maximum distance value is specified.
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| For a given query object Q ∈ D and a maximum search distance
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| r(Q), the range query '''range'''(Q, r(Q)) selects all the indexed objects Oj such that d(Oj, Q) ≤ r(Q).<ref name="Univ Bologna Range">{{cite web|title=Indexing Metric Spaces with M-tree|url=http://www-db.deis.unibo.it/research/papers/SEBD97.pdf|work=Department of Computer Science and Engineering|publisher=University of Bologna|accessdate=19 November 2013|author=P. Ciaccia, M. Patella, F. Rabitti, P. Zezula|page=3}}</ref>
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| Algorithm RangeSearch starts from the root node and recursively traverses all the paths which cannot be excluded from leading to qualifying objects.
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| {{algorithm-begin|name=Insert}}
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| Input: Node <math>N</math> of M-Tree <math>MT</math>, <math>Q</math>: query object, <math>r(Q)</math>: search radius
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| Output: all the DB objects such that <math>d(Oj, Q)</math> ≤ <math>r(Q)</math>
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| { let <math>O_{p}</math> be the parent object of node <math>N</math>;
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| '''if''' <math>N</math> is not a leaf
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| '''then''' { for each <math>entry(O_{r})</math> in N do:
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| '''if''' | <math>d(O_{p}, Q)</math> − <math>d(O_{r}, O_{p})</math> | ≤ <math>r(Q) +r(O_{r})</math>
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| '''then''' { Compute <math>d(O_{r}, Q)</math>;
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| '''if''' <math>d(O_{r}, Q)</math> ≤ <math>r(Q) +r(O_{r})</math>
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| '''then''' <math>RangeSearch(*ptr(T(O_{r})),Q,r(Q))</math>; }}
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| '''else''' { for each <math>entry(O_{j})</math> in <math>N</math> do:
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| '''if''' | <math>d(O_{p}, Q)</math> − <math>d(O_{j}, O_{p})</math> | ≤ <math>r(Q)</math>
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| '''then''' { Compute <math>d(O_{j}, Q)</math>;
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| '''if''' <math>d(O_{j}, Q)</math> ≤ <math>r(Q)</math>
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| '''then''' add <math>oid(O_{j})</math> to the result; }}}
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| {{algorithm-end}}
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| <math>oid(O_{j})</math> is the identifier of the object which resides on a separate data file.
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| <math>T(O_{r})</math> is a sub-tree – the covering tree of <math>O_{r}</math>
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| | |
| === k-NN queries ===
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| K Nearest Neighbor (k-NN) query takes the cardinality of the input set as an input perimeter. For a given query object Q ∈ D and an
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| integer k ≥ 1, the k-NN query NN(Q, k) selects the k indexed objects which have the shortest distance from Q, according to the distance function d.
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| <ref name="Univ Bologna Range"/>
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| {{Empty section|date=January 2011}}
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| ==See also==
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| * [[Segment tree]]
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| * [[Interval tree]] - A degenerate R-Tree for 1 dimension (usually time).
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| * [[Bounding volume hierarchy]]
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| * [[Spatial index]]
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| * [[GiST]]
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| ==References==
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| {{reflist}}
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| {{CS-Trees}}
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| {{DEFAULTSORT:M-Tree}}
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| [[Category:Trees (data structures)]]
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| [[Category:Database index techniques]]
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| [[Category:Geometric data structures]]
| |
There are many online companies that write custom scholarship essays for students. Term Paper Help As we have discussed before that, if you need any sort of help regarding term paper help, so you can any time contact with us and we will tackle your problems. This is a thought or hypothesis that you will either support or refute in your essay. You need to learn to avoid mistakes and focus more on quality. There is a strong possibility that two students of the same class have bought the same essay.
There are three major elements of deductive essays that one should consider while writing deductive essays. However, there are essay writing companies which can help these students survive college. Contrary to early reports from the Washington POST, the SAT essay is not dead yet. Every good essay begins with a thought or argument called 'a thesis. They should be followed and tweaked so that you are producing the quality content your readers deserve.
Think about how you are going to complete the task whilst simultaneously maximising the available marks in each section. com will provide a very good opportunity for college students to get involved in a greater capacity in writing their essays. Narrate the whole story through writing in a way that can be easily understood by the reader. Think about how this reflects ideas in the poem, for example a very uneven structure could represent ideas of chaos or lack of control. A student always wants a unique and well-structured piece of composition so that he or she can present it confidently in front of the tutors and get high scores.
This way will assist as it is so complicated to detect mistakes in your work. There is customer care team that is available to the customers at any hour of the day. Likewise to the similarities, the next part of writing a compare and contrast essay is to find out the differences among them. In the Academy of Art New Delhi the students have the opportunities to get the educational degrees in Interior designing, retail designing and visual merchandising. This is important to ensure that you buy essay papers that are right, appropriate, and of high quality.
If you have any kind of questions relating to in which and also the way to use do my homework, you are able to email us with the web site. Write a quick schedule to help you allocate your time wisely: list the days you have left and the time during the day you will be able to work. should always be the principal priority of a company. You may have problems in understanding the subjects. Our essay writing website is the best original essay writing service one can come across while searching for original papers, original essays, original term papers, original research papers, original academic papers, original thesis papers or original English essay writing. You should conclude the essay by focusing on the main purpose of the essay.