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

A new approach to ensemble learning is introduced that takes ranking rather than classification as fundamental, leading to models on the symmetric group and its cosets. The approach uses a generalization of the Mallows model on permutations to combine multiple input rankings. Applications include the task of combining the output of multiple search engines and multiclass or multilabel classification, where a set of input classifiers is viewed as generating a ranking of class labels.

We investigate the simplest class of hyperdeterminants de ned by Cayley in the case of Hankel hypermatrices (tensors of the form A i 1 i 2 :::i k = f(i 1 +i 2 + +i k )). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg's original formula amounts to the evaluation of all Hankel hyperdeterminants built from the moments of the Jacobi polynomials. Many higher-dimensional analogues of classical Hankel determinants are evaluated in closed form. The Toeplitz case is also briey discussed. In physical terms, both cases are related to the partition functions of one-dimensional Coulomb systems with logarithmic potential.

Search landscape analysis has become a central tool for analysing the dependency of the performance of stochastic local search algorithms on structural aspects of the spaces being searched. Central to search landscape analysis is the notion of distance between candidate solutions. This distance depends on some underlying basic operator and it is defined as the minimum number of operations that need to be applied to one candidate solution for transforming it into another one. For operations on candidate solutions that are represented by permutations, in almost all researches on search landscape analysis surrogate distance measures are applied, although efficient algorithms exist in many cases for computing the exact distances. This discrepancy is probably due to the fact that these efficient algorithms are not very widely known. In this article, we review algorithms for computing distances on permutations for the most widely applied operators and present simulation results that compare the exact distances to commonly used approximations.

We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials. 1

A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.

The purpose of this paper is to exhibit clearly how the “graphical condensation” identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn–Percus method for the enumeration of matchings. Knuth termed the relevant identities “overlapping Pfaffian ” identities and the key concept of proof “superpositions of matchings”. In our uniform presentation of the material, we also give an apparently unpublished general “overlapping Pfaffian ” identity of Krattenthaler.

We show that a very elementary trick allows to generalize a theorem of Linström to higher determinants. As a special case, one recovers some results due to Lehmer and Haukkannen on hyperdeterminants of GCD matrices. 1