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, 2-3 trees, and B-trees. 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 93-0765. e-mail: rbaeza@dcc.uchile.cl 1 Introduction Search trees are one of the most used data structures t...

We present a new overflow technique for B-trees. 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 non-uniform 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 bucket-based 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 B-tree 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...

In this paper we complete the analysis done by Ramakrishna and Mukhopadhyay for a data node in the Bounded Disorder (BD) file organization of Litwin and Lomet, by introducing the B-tree index into the model. Also, we extend the analysis to the case of BD files with two partial expansions as proposed by Lomet. Our main contribution is a detailed analysis of search and insertion costs, and its comparison with B + -trees. 1 Introduction Nowadays there are two main file organizations: hashing and tree indexing. New hashing techniques achieve single access retrieval, but are very inefficient for range search or key sequential access. On the other hand tree indices preserve the key order with a higher search cost. Litwin and Lomet [9] proposed the Bounded Disorder (BD) file organization to combine the advantages of both methods. This paper complements the analysis presented by Ramakrishna and Mukhopadhyay [14] concerning the performance of BD files, by including the index in their model. ...

A modeling technique, the Capitalist model, is outlined for analyzing multi-dimensional file structures. It is particularly appropriate where the data keys may have non-uniform data distributions. The basis of the model is to assume that the current distribution of data in an existing file is a good predictor of the underlying "true" distribution. The method is applied to formal analysis of the BANG and NIBGF directory structures. The average cost for search and insertion is found to be logarithmic in the file size. The order constant is quite small and depends on the capacity of a bucket. Simulation confirms the analytic results. This first use of the Capitalist model suggests its usefulness to the analysis of other multidimensional file structures.