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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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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...
A Cost Model for Path Expressions in ObjectOriented Queries
 Journal of Database Management
, 1996
"... Query processing remains one of the important challenges of ObjectOriented Database Management Systems. Cost based query optimization involves creating alternative executing plans for a given query and executing the least costly one within a cost model framework. In ObjectOriented Database Managem ..."
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Cited by 3 (1 self)
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Query processing remains one of the important challenges of ObjectOriented Database Management Systems. Cost based query optimization involves creating alternative executing plans for a given query and executing the least costly one within a cost model framework. In ObjectOriented Database Management Systems (OODBMSs) objects may store references to other objects (precomputed joins), and path expressions are used in query languages. Although the cost fomulas for explicit joins and the selectivities of attributes and joins are wellknown in the relational model, there is no similar work involving path expressions for OODBMSs. However in order to optimize objectoriented queries involving path expressions, a cost model is essential. This information is necessary for deciding whether to use pointer chasing or to convert the path expressions into explicit joins and also for deciding the execution order of path expressions. In this paper, we provide a cost model that includes the formulas...
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...
Fibonacci Numbers with Subscripts 2 n k, u
"... Under the assumption that all of the 32 trees of height h are equally probable, it is shown that in a 32 tree of height h the expected number of keys is (.72162)3 ^ and the expected number of internal nodes is (.48061)3^. ..."
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Under the assumption that all of the 32 trees of height h are equally probable, it is shown that in a 32 tree of height h the expected number of keys is (.72162)3 ^ and the expected number of internal nodes is (.48061)3^.