Random B Trees With Inserts And Deletes

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Random B Trees With Inserts And Deletes
Theodore Johnson
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, A2p-i) p + ;■ - 1 IS odd Note that not every node order has the chance of gaining on a merge operation. In particular, if p is even, then (3p — 2)/2 is the largest order of nodes that will gain; if p is odd, then (3p — l)/2 is the largest order of nodes that will gain.
Since the structure of the evolution of the B-tree is different if p is odd or even, let us examine first the case when p is even. An order t node will be merged with its neighbor if its neighbor is of order p and receives a de
...lete (assume a node merges with its right neighbor, except if the node is the rightmost node, in which case it merges with its left neighbor). The probability that a node of order i is the neighbor of the merging node is Ai(L)/V{L). The result of the merge operation is two nodes of order {i -\- p— l)/2, or a node of order (i -I- p)/2 and a node of order {i + p — 2)/2. Therefore, one node of order j will be created if a node of order 2j — p or a node or order 2i — p -I- 2 is merged, and two nodes of order i will be created if a node of order 2j - p -I- 1 is merged.

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