The space utilization of B-tree nodes determines the number of levels in the B-tree and hence its performance. Until now, the only analytical aid to the determination of a B-tree's utilization has been the analysis by Yao and related work. Yao showed that the utilization of B-tree nodes under pure inserts is 69%. We derive analytically and verify by simulation the utilization of B-tree nodes constructed from a mixture of insert and delete operations. Assuming that nodes only merge (i.e. are freed) when they are empty we show that the utilization is 39% when the number of inserts is the same as the number of deletes. However, if there are just 5% more inserts than deletes, then the utilization is over 62%. We also calculate the probability of splitting and merging. We derive a simple rule-of-thumb that accurately calculates the probability of splitting. We also model B-trees that merge half-empty nodes. The utilization of merge-at-half B-trees is slightly larger than the utilization of ...

This thesis develops a validated model of concurrent data structure algorithm performance, concentrating on concurrent B-trees. The thesis first develops two analytical tools, which are explained in the next two paragraphs, for the analysis. Yao showed that the space utilization of a B-tree built from random inserts is 69%. Assuming that nodes merge only when empty, we show that the utilization is 39% when the number of insert and delete operations is the same. However, if there are just 5% more inserts than deletes, then the utilization is at least 62%. In addition to the utilization, we calculate the probabilities of splitting and merging, important parameters for calculating concurrent B-tree algorithm performance. We compare merge-at-empty B-trees with merge-at-half B-trees. We conclude that merge-at-empty Btrees have a slightly lower space utilization but a much lower restructuring rate than merge-at-half B-trees, making merge-at-empty B-trees preferable for concurrent B-tree algo...

This paper describes algorithms for key deletion in B+-trees. There are published algorithms and pseudocode for searching and inserting keys, but deletion, due to its greater complexity and perceived lesser importance, is glossed over completely or left as an exercise to the reader. To remedy this situation, we provide a well documented flowchart, algorithm, and pseudo-code for deletion, their relation to search and insertion algorithms, and a reference to a freely available, complete B+-tree library written in the C programming language.

A fast B-tree based indexing algorithm is presented. In some applications, such as full text indexing or indexing of very large tables, the new algorithm can be orders of magnitude faster than conventional B-tree insertion algorithms, while still allowing concurrent access. A similar algorithm can be used for deletion.