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Btrees with inserts and deletes: Why freeatempty is better than mergeathalf
 Journal of Computer and System Sciences
, 1993
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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...
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 11 (5 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...
A uniform model for the storage utilization of Btreelike structures
"... By using the method of Riordan arrays we find the asymptotic value of the expected storage utilization in a model of uniform Btreelike structures proposed by Gupta and Srinivasan, thus solving the occupancy problem for that model. Keywords: analysis of algorithms, Btrees, Riordan arrays, storage ..."
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By using the method of Riordan arrays we find the asymptotic value of the expected storage utilization in a model of uniform Btreelike structures proposed by Gupta and Srinivasan, thus solving the occupancy problem for that model. Keywords: analysis of algorithms, Btrees, Riordan arrays, storage utilization. 1 Introduction Btrees are one of the most frequently used structures for storing information in a two level storage. Since their introduction in the early '70, they have been widely studied together with their main memory companion, the 23trees, and therefore a vast literature exists, in whichtheir performance is analyzed. Just to give some examples, we quote here the papers by BaezaYates [1], Chu and Knott [3], Quitzow and Klopprogge [9] and Wright [14], which all refer to a distribution in which key permutations are all equally likely. The problem is quite hard, and therefore several approximate models have been proposed, in order to simplify the analysis, especially con...