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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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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...
HigherOrder Analysis of 23 Trees
 Int. J. Foundations Comp. Sci
, 1995
"... We present a fourthorder fringe analysis for the expected behavior of 23 trees, which includes 97% of the elements in the tree. It is accomplished by exploiting the structure of the transition matrix. Our results improve a number of bounds, in particular the bounds on the expected number of nodes ..."
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We present a fourthorder fringe analysis for the expected behavior of 23 trees, which includes 97% of the elements in the tree. It is accomplished by exploiting the structure of the transition matrix. Our results improve a number of bounds, in particular the bounds on the expected number of nodes and the expected space utilization. We also study 23 trees built by using overflow techniques. 1 Introduction Fringe analysis was formally introduced by Yao in 1974 [Yao74, Yao78] as a method to analyze search trees that considers only the bottom part or fringe of the tree. From the behavior of the subtrees in the fringe, it is possible to obtain bounds on most complexity measures for the complete tree, as well as some exact results. Classical fringe analysis considers only insertions. The model assumes that the n! possible permutations of the n keys used as input are equally likely. A search tree built under this model is called a random tree. This is equivalent to saying that the nth in...
Persistently Cached BTrees
, 2001
"... This paper presents an approach to enhancing Btree indexing performance by using a replication technique called persistent caching. A notable feature of the approach is its compatibility with ordinary Btrees# it exploits only the otherwise unused area of each Btree page, and the basic behavior ..."
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This paper presents an approach to enhancing Btree indexing performance by using a replication technique called persistent caching. A notable feature of the approach is its compatibility with ordinary Btrees# it exploits only the otherwise unused area of each Btree page, and the basic behavior of Btrees need not be changed. This paper evaluates the performance of persistently cached Btrees by showing the result of mathematical analysis and of experimental investigations. Keywords: Btrees, B + trees, database management system, secondary storage management, replication, persistentcaching, complex objects, indexing structure. 1