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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 14 (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...
Fringe Analysis Revisited
"... Fringe analysis is a technique used to study the average behavior of search trees. In this paper we survey the main results regarding this technique, and we improve a previous asymptotic theorem. At the same time we present new developments and applications of the theory which allow improvements in ..."
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Cited by 12 (6 self)
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Fringe analysis is a technique used to study the average behavior of search trees. In this paper we survey the main results regarding this technique, and we improve a previous asymptotic theorem. At the same time we present new developments and applications of the theory which allow improvements in several bounds on the behavior of search trees. Our examples cover binary search trees, AVL trees, 23 trees, and Btrees. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity ]: Nonnumerical Algorithms and Problems  computations on discrete structures; sorting and searching; E.1 [Data Structures]; trees. Contents 1 Introduction 2 2 The Theory of Fringe Analysis 4 3 Weakly Closed Collections 9 4 Including the Level Information 11 5 Fringe Analysis, Markov Chains, and Urn Processes 13 This work was partially funded by Research Grant FONDECYT 930765. email: rbaeza@dcc.uchile.cl 1 Introduction Search trees are one of the most used data structures t...
An Adaptive Overflow Technique for Btrees
 Extending Data Base Technology Conference (EDBT 90
, 1990
"... We present a new overflow technique for Btrees. The technique is a hybrid of partial expansions and unbalanced splits. This technique is asymmetric and adaptive. Considering a growing file (only insertions), the storage utilization is 77% for random keys, 70% for sorted keys, and over 75% for nonu ..."
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Cited by 1 (1 self)
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We present a new overflow technique for Btrees. The technique is a hybrid of partial expansions and unbalanced splits. This technique is asymmetric and adaptive. Considering a growing file (only insertions), the storage utilization is 77% for random keys, 70% for sorted keys, and over 75% for nonuniform distributed keys. Similar results are achieved when we have deletions mixed with insertions. One of the main properties of this technique is that the storage utilization is very stable with respect to changes of the data distribution. This technique may be used for other bucketbased file structures, like extendible hashing or bounded disorder files. 1 Introduction The B + tree is one of the most widely used file organizations. In a B + tree all the information is stored at the lowest level (buckets), and the upper levels are a Btree index. File growth is handled by bucket splitting, that is, when a bucket overflows, a new bucket is allocated and half of the records from the o...