Earlier we studied balanced binary search trees, such as AVL trees, that relied on rotation for balancing trees that were only one-level away from balance. An alternative method for balancing is to use multi-way branching trees like B-Trees or 2-3 Trees.

Key properties to multiway balanced trees are:

• Branching nodes in the same tree can have different branching factors. In a binary search tree every brancing node has a brancing factor of 2.
• For a node with branching factor of n, there are (n-1) key values, and the values in nodes in sub trees obey invariants about which relate to the key values.
• There is an upper bound to the branching factor. When the upper bound is reached, the node is split into 2-nodes each with roughly one half the branching factor.
• Trees are balanced by adjusting the branching factor or some of the nodes in a tree that is only slightly out of balance.

A multi-way balance tree of order n has a maximum branching factor of n.

Two common kinds of multiway balanced trees are:

• B-Trees.
  1. Often used in databases, where each node maps to a distinct disk page.
  2. Since Disk accesses take several orders of magnitude more time to access than memory accesses, much time can be saved by making the nodes have a high order, thus making the height of the tree very small.
  3. The shallower the tree, the fewer disk accesses necessary and the faster the search.
  4. Disk drives often read a large amount of data at a time so this correlates with a large Node size as well.
• 2-3 Trees are multi-way trees with order 3.
  1. Since the order is small and fixed, the code to implement them is often simpler.
  2. Intra-node search is quick since the node size is small.
  3. Often used for main memory data rather than data stored on disks.

Back to the Daily Record.

Back to the class web-page.