# balanced tree

## balanced tree

(algorithm)
An optimisation of a tree which aims to keep equal numbers of items on each subtree of each node so as to minimise the maximum path from the root to any leaf node. As items are inserted and deleted, the tree is restructured to keep the nodes balanced and the search paths uniform. Such an algorithm is appropriate where the overheads of the reorganisation on update are outweighed by the benefits of faster search.

A B-tree is a kind of balanced tree that can have more than two subtrees at each node (i.e. one that is not restricted to being a binary tree).
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In a strictly balanced tree, the value range of balance factor should only be [-1,1], which is the balance criterion of the original AVL tree.
Definition 2: The height difference of any one node in the tree or subtree is not greater than 1, so that the tree is a balanced tree.
This results in a balanced tree construction, in which none of the nodes are overburdened.
That means the balanced tree topology construction approach significantly improves the network lifetime and causes only very low extra data latency overhead when doing that.
A more balanced tree will reduce the expected travel cost, but how can the structure be rebalanced without losing clustering information?
If the tree is not a leaner, it may be possible to use the felling cuts to bring it down where you want it--but don't bet the farm on it; if you cut wood long enough, eventually an apparently straight, well balanced tree will surprise you.
Note that we have used informally the expression "balanced tree", without specifying its definition.
Given an unbalanced tree T, we construct a balanced tree T' from T.
I ranges from zero for a perfectly balanced tree to one for a perfectly imbalanced tree [ILLUSTRATION FOR FIGURE 1 OMITTED].
Balanced tree algorithms rearrange the tree as operations are performed to maintain certain balance conditions and assure good performance.
Because there is more than one way to make the same balanced tree, the Markov model predicts a relatively high proportion of balanced trees.
The global balancing algorithms inspect all of the nodes in a tree in order to reconstruct a balanced tree. The global strategies produce either a perfectly balanced tree [2, 3, 9] or a route balanced tree [4, 11] (i.e., a tree with minimal internal path length).

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