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...

ABSTRACX A new technique, based on virtual backpointers. for local concurrent error detection and correction in linked data structures is presented in this paper. Two new data structures, the Virtual Double-Linked List, and the B-Tree with Virtual Backpointers. are described. For these structures, double errors can be detected in O(1) time and errors detected during forward moves can be corrected in O(1) time. The application of a concurrent auditor process to data structure error I detection and correction is analyzed, and an implementation is described. to determine the effect on the mean time to failure of a multi-user shared-database system. The implementation utilizes a Sequent shared-memory multiprocessor system operating on a shared database of Virtual Double-1 LinkedLists. l Idex Terms- concurrent error detection, data structures. concurrent structure checking