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...

A fast B-tree based indexing algorithm is presented. In some applications, such as full text indexing or indexing of very large tables, the new algorithm can be orders of magnitude faster than conventional B-tree insertion algorithms, while still allowing concurrent access. A similar algorithm can be used for deletion.

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. ...

We present a fourth-order fringe analysis for the expected behavior of 2-3 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 2-3 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 n-th in...