The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.

The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems for which the information is partial, noisy, and priced. Such problems arise in many areas including economics, physics, human and robotic vision, scientific and engineering computation, geophysics, decision theory, signal processing and control theory.

Algorithms play a central role both in the theory and in the practice of computing. The goal of the authors was to write a textbook that would not trivialize the subject but would still be readable by most students on their own. The book contains over 120 exercises. Some of them are drills; others make important points about the material covered in the text or introduce new algorithms not covered there. The book also provides programming projects. From the Table of Contents: Chapter 1: Basic knowledge of Mathematics, Relations, Recurrence relation and Solution techniques, Function and Growth of functions. Chapter 2: Different Sorting Techniques and their analysis. Chapter 3: Greedy approach, Dynamic Programming, Brach and Bound techniques, Backtracking and Problems, Amortized analysis, and Order Statics. Chapter 4: Graph algorithms, BFS, DFS, Spanning Tree, Flow Maximization Algorithms. Shortest Path Algorithms. Chapter 5: Binary search tree, Red black Tree, Binomial heap, B-Tree and Fibonacci Heap. Chapter 6: Approximation Algorithms, Sorting Networks, Matrix operations, Fast Fourier Transformation, Number theoretic Algorithm, Computational geometry Randomized Algorithms, String matching, NP-Hard, NP-Completeness, Cooks theorem.

This book contains five essays on the complexity of continuous problems, written for a wider audience. The first four essays are based on talks presented in 2008 when Henryk Wozniakowski received an honorary doctoral degree from the Friedrich Schiller University of Jena. The focus is on the introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of high-dimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of information-based complexity addressed to a general readership.

The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

This book constitutes the proceedings of the 18th Annual European Symposium on Algorithms, held in Liverpool, UK in September 2010.

This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.