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M-tree

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Project Owner : vani.R
Created Date : Thu, 15/03/2012 - 13:09
Project Description :

 

Components

An M-Tree has these components and sub-components:

  1. Root.
    1. Routing object O.
    2. Radius Or.
    3. A set of Nodes or (exclusive) Leafs.
  2. Node.
    1. Routing object Or.
    2. Radius Or.
    3. Distance from this node to its parent Op.
    4. A set of Nodes or (exclusive) Leafs.
  3. Leaf.
    1. Routing object O.
    2. Radius Or.
    3. Distance from this leaf to its parent Op.
    4. Objects.
  4. Objects.
    1. Feature value (usually a d-dimensional vector).

[edit]Insert

The main idea is first to find a leaf node N where the new object O belongs. If N is not full then just attach it to N. If N is full then invoke a method to split N. The algorithm is as follows:

	Algorithm Insert
  Input: Node 
N
	of M-Tree 
MT
	, Entry 
O_{n}
	Output: A new instance of 
MT
	containing all entries in original 
MT
	plus 
O_{n}
	
	
N_{e}
	← Entries of node 
N
	if 
N
	is not a leaf then
  {
       /*Look for entries that the new object fits into*/
       let 
N_{in}
	be entries such that 
d(O_{r}, O_{n}) <= r(O_{r})
	if 
N_{in}
	is not empty then
       {
          /*If there are one or more entry, then look for an entry such that is closer to the new object*/
          let be 
O_{r}^{*} \in N_{in}
	such that 
d(O_{r}^{*}, O_{n})
	is minimum
       }
       else
       {
          /*If there are no such entry, then look for an entry with minimal distance from its edge to the new object*/
          let be 
O_{r}^{*} \in N_{in}
	such that 
d(O_{r}^{*}, O_{n}) - r(O_{r})
	is minimum
          /*Upgrade the new radii of the entry*/
          
r(O_{r}^{*})
	= 
d(O_{r}^{*}, O_{n})
	}
       /*Continue inserting in the next level*/
       return insert(
T(O_{r}^{*})
	, 
O_{n}
	);
  else
  {
       /*If the node has capacity then just insert the new object*/
       if 
N
	is not full then
       {  store(
N
	, 
O_{n}
	)   }
       /*The node is at full capacity, then it is needed to do a new split in this level*/
       else
       {  split(
N
	, 
O_{n}
	) }
  }


Split

If the split method arrives to the root of the tree, then it choose two routing objects from N, and creates two new nodes containing all the objects in original N, and store them into the new root. If split methods arrives to a node N that is not the root of the tree, the method choose two new routing objects from N, re-arrange every routing object in N in two new nodes N_{1} and N_{2}, and store this new nodes in the parent node N_{p} of original N. The split must be repeated if N_{p} has not enough capacity to store N_{2}. The algorithm is as follow:

		Algorithm Split
  Input: Node 
N
		of M-Tree 
MT
		, Entry 
O_{n}
		Output: A new instance of 
MT
		containing a new partition.
		/*The new routing objects are now all those in the node plus the new routing object*/
  let be 
NN
		entries of 
N \cup O
		if 
N
		is not the root then
  {
     /*Get the parent node and the parent routing object*/
     let 
O_{p}
		be the parent routing object of 
N
		let 
N_{p}
		be the parent node of 
N
		}
  /*This node will contain part of the objects of the node to be split*/
  Create a new node 
N'
		/*Promote two routing objects from the node to be split, to be new routing objects*/
  Promote(
N
		, 
O_{p1}
		, 
O_{p2}
		)
  /*Choose which objects from the node being split will act as new routing objects*/
  Partition(
N
		, 
O_{p1}
		, 
O_{p2}
		, 
N_{1}
		, 
N_{2}
		)
  /*Store entries in each new routing object*/
  Store 
N_{1}
		's entries in 
N
		and 
N_{2}
		's entries in 
N'
		if 
N
		is the current root then
  {
      /*Create a new node and set it as new root and store the new routing objects*/
      Create a new root node 
N_{p}
		Store 
O_{p1}
		and 
O_{p2}
		in 
N_{p}
		}
  else
  {
      /*Now use the parent rouing object to store one of the new objects*/
      Replace entry 
O_{p}
		with entry 
O_{p1}
		in 
N_{p}
		if 
N_{p}
		is no full then
      {
          /*The second routinb object is stored in the parent only if it has free capacity*/
          Store 
O_{p2}
		in 
N_{p}
		}
      else
      {
           /*If there is no free capacity then split the level up*/
           split(
N_{p}
		, 
O_{p2}
		)
      }
  }
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