Expanded Half
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EXPANDED HALF SHELL
Expanded Insert Algorithm in a B*Tree
A B*Tree is a variant of the B-Tree, and was named by Douglas Comer and introduced by Donald Knuth. In a B*Tree, all nodes except the root are required to be at least two-thirds full, unlike B-Tree which is just half full. The frequency of splitting node is decreased by delaying a split. How? By splitting not one node into two but two nodes into three. The average utilization of a B* tree is 81% (Leung 1984)
A split in a B*Tree is delayed if redistribution of the key values of a node and its sibling is done when the node overflows. If the sibling is also full, a split occurs: One new node is created, the keys from the node and its siblings (along with the separating keys from the parent) are evenly divided among three nodes, and two separating keys are put into the parent. All three nodes participating in the split are guaranteed to be two-thirds full.
To reduce the frequency of splitting nodes, a possible accommodation of a key value from an overflowing terminal node to its nearest siblings should be considered. If accommodation of a key value in an overflowing terminal node is not possible, that is, both nearest siblings are also full, a split do not take place, rather, a redistribution of key values takes place.
Properties of a B*Tree:
- Interior or non-leaf node with N key values contains N+1 links.
- The root node contains at least 1 key value and at most 2ë(2M-2)/3û key values of order M.
- All non-root nodes contain at least é(2M-1)/3ù - 1 key values and at most M-1 key values.
The expanded insert algorithm is an improvement of the original insert algorithm. Results from the simulations indicated a positive outcome. Possible effects of the expanded insert algorithm were as follows:
- Reduction in the occurrences of nodes overflowing;
- Reduction of action taken when a node overflows;
- Reduction of nodes used; and
- Reduction of height for the B*Tree.
All of these positive outcome would transcend to a more compact B*Tree which can yield to an optimal utilization of terminal nodes with a higher probability of having more than 2/3 full capacity.
As a result, the expanded insert algorithm can achieve a far more favorable priori and posteriori estimates.
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