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...

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. ...