Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems --- Sorting and Searching; E.5 [Data]: Files --- Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics --- Probabilistic algorithms; E.2 [Data Storage Representation]: Composite structures, linked representations. General Terms: Algorithms, Theory. Additional Key Words and Phrases: Adaptive sorting algorithms, Comparison trees, Measures of disorder, Nearly sorted sequences, Randomized algorithms. A Survey of Adaptive Sorting Algorithms 2 CONTENTS INTRODUCTION I.1 Optimal adaptivity I.2 Measures of disorder I.3 Organization of the paper 1.WORST-CASE ADAPTIVE (INTERNAL) SORTING ALGORITHMS 1.1 Generic Sort 1.2 Cook--Kim division 1.3 Partition Sort 1.4 Exponential Search 1.5 Adaptive Merging 2.EXPECTED-CASE ADAPTIV

The availability of large main memories and the new technologies for disk drives have modified the models for external sorting and have renewed interest in their study. Little is known about the performance of traditional and more recent sorting methods on nearly sorted files although such files are common in practice. ffl We confirm mathematically that the lengths of the runs created by replacement selection during the first phase of external sorting increases as the order in the input file increases. Previous work has concentrated on the expected length of initial runs when all input files are equally likely to occur. It has long been accepted that when an input file has little disorder, the lengths of the generated runs will be long. We establish such results for two measures of disorder, namely, the number of ascending runs and the maximal distance between inversions. ffl We demonstrate that, during the merging phase, the floating-buffers technique not only reduces the sorting ti...