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 algorithm selection problem aims at selecting the best algorithm for a given computational problem instance according to some characteristics of the instance. In this dissertation, we first introduce some results from theoretical investigation of the algorithm selection problem. We show, by Rice's theorem, the nonexistence of an automatic algorithm selection program based only on the description of the input instance and the competing algorithms. We also describe an abstract theoretical framework of instance hardness and algorithm performance based on Kolmogorov complexity to show that algorithm selection for search is also incomputable. Driven by the theoretical results, we propose a machine learning-based inductive approach using experimental algorithmic methods and machine learning techniques to solve the algorithm selection problem. Experimentally, we have

Yamasaki and Doshita have de ned an extension of the class of propositional Horn formulas; later, Gallo and Scutella generalized this class to a hierarchy 0 1 : : : k : : :, where 0 is the set of Horn formulas and 1 is the class of Yamasaki and Doshita. For any xed k, the propositional formulas in k can be recognized in polynomial time, and the satis ability problem for k formulas can be solved in polynomial time. A possible way of extending these tractable subclasses of the satis ability problem is to consider renamings: a renaming of a formula is obtained by replacing for some variables all their positive occurrences by negative occurrences and vice versa.