M-way Trees

 M- Way Trees

  • A multi-way tree is a tree that can have more than two children

  • A multi-way tree of order m (number or a **m-way tree) is one in which a tree can have m children.

  • An m-way search tree is a m-way tree in which:

a) Each node has m children and m-1 key fields

b) The keys in each node are in ascending order.

c) The keys in the first i children are smaller than the ith key

d) The keys in the last m-i children are larger than the ith key

  • In a binary search tree, m=2. So it has one value and two sub trees.

  • The figure above is a m-way search tree of order 3.

  • M-way search trees give the same advantages to m-way trees that binary search trees gave to binary trees - they provide fast information retrieval and update.

  • However, they also have the same problems that binary search trees had - they can become unbalanced, which means that the construction of the tree becomes of vital importance.

  • In m-way search tree, each sub-tree is also a m-way search tree and follows the same rules.

  • An extension of a multi-way search tree of order m is a B-tree of order m.

  • This type of tree will be used when the data to be accessed / stored is located on secondary storage devices because they allow for large amounts of data to be stored in a node.

 

Example: A Four Way Tree

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