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Btrees with Inserts and Deletes: Why Freeatempty is Better Than Mergeathalf
 Journal of Computer and System Sciences
, 1992
"... The space utilization of Btree nodes determines the number of levels in the Btree and hence its performance. Until now, the only analytical aid to the determination of a Btree's utilization has been the analysis by Yao and related work. Yao showed that the utilization of Btree nodes under pure i ..."
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Cited by 18 (0 self)
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The space utilization of Btree nodes determines the number of levels in the Btree and hence its performance. Until now, the only analytical aid to the determination of a Btree's utilization has been the analysis by Yao and related work. Yao showed that the utilization of Btree nodes under pure inserts is 69%. We derive analytically and verify by simulation the utilization of Btree 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 ruleofthumb that accurately calculates the probability of splitting. We also model Btrees that merge halfempty nodes. The utilization of mergeathalf Btrees is slightly larger than the utilization of ...
The Performance of Concurrent Data Structure Algorithms
 Transactions on Database Systems
, 1994
"... This thesis develops a validated model of concurrent data structure algorithm performance, concentrating on concurrent Btrees. 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 Btree built fr ..."
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Cited by 13 (9 self)
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This thesis develops a validated model of concurrent data structure algorithm performance, concentrating on concurrent Btrees. 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 Btree 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 Btree algorithm performance. We compare mergeatempty Btrees with mergeathalf Btrees. We conclude that mergeatempty Btrees have a slightly lower space utilization but a much lower restructuring rate than mergeathalf Btrees, making mergeatempty Btrees preferable for concurrent Btree algo...
Implementing Deletion in B+Trees
"... 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 s ..."
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Cited by 3 (0 self)
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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 pseudocode 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.
An Algorithm for Full Text Indexing
, 1992
"... A fast Btree 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 Btree insertion algorithms, while still allowing concurrent access. A similar algorithm c ..."
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Cited by 2 (0 self)
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A fast Btree 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 Btree insertion algorithms, while still allowing concurrent access. A similar algorithm can be used for deletion.