Boolean Function Complexity

Advances and Frontiers

Author: Stasys Jukna

Publisher: Springer Science & Business Media

ISBN: 3642245080

Category: Mathematics

Page: 620

View: 3422

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.

Extremal Combinatorics

With Applications in Computer Science

Author: Stasys Jukna

Publisher: Springer Science & Business Media

ISBN: 3662046504

Category: Computers

Page: 378

View: 1277

This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.

Bioinspired Computation in Combinatorial Optimization

Algorithms and Their Computational Complexity

Author: Frank Neumann,Carsten Witt

Publisher: Springer Science & Business Media

ISBN: 3642165443

Category: Mathematics

Page: 216

View: 3499

Bioinspired computation methods such as evolutionary algorithms and ant colony optimization are being applied successfully to complex engineering problems and to problems from combinatorial optimization, and with this comes the requirement to more fully understand the computational complexity of these search heuristics. This is the first textbook covering the most important results achieved in this area. The authors study the computational complexity of bioinspired computation and show how runtime behavior can be analyzed in a rigorous way using some of the best-known combinatorial optimization problems -- minimum spanning trees, shortest paths, maximum matching, covering and scheduling problems. A feature of the book is the separate treatment of single- and multiobjective problems, the latter a domain where the development of the underlying theory seems to be lagging practical successes. This book will be very valuable for teaching courses on bioinspired computation and combinatorial optimization. Researchers will also benefit as the presentation of the theory covers the most important developments in the field over the last 10 years. Finally, with a focus on well-studied combinatorial optimization problems rather than toy problems, the book will also be very valuable for practitioners in this field.

Computational Complexity

A Modern Approach

Author: Sanjeev Arora,Boaz Barak

Publisher: Cambridge University Press

ISBN: 0521424267

Category: Computers

Page: 579

View: 9465

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

Advances in Network Complexity

Author: Matthias Dehmer,Abbe Mowshowitz,Frank Emmert-Streib

Publisher: John Wiley & Sons

ISBN: 3527670483

Category: Medical

Page: 308

View: 2944

A well-balanced overview of mathematical approaches to complex systems ranging from applications in chemistry and ecology to basic research questions on network complexity. Matthias Dehmer, Abbe Mowshowitz, and Frank Emmert-Streib, well-known pioneers in the fi eld, have edited this volume with a view to balancing classical and modern approaches to ensure broad coverage of contemporary research problems. The book is a valuable addition to the literature and a must-have for anyone dealing with network compleaity and complexity issues.

Computing and Combinatorics

20th International Conference, COCOON 2014, Atlanta, GA, USA, August 4-6, 2014, Proceedings

Author: Zhipeng Cai,Alexander Zelikovsky,Anu G. Bourgeois

Publisher: Springer

ISBN: 3319087835

Category: Computers

Page: 692

View: 7617

This book constitutes the refereed proceedings of the 20th International Conference on Computing and Combinatorics, COCOON 2014, held in Atlanta, GA, USA, in August 2014. The 51 revised full papers presented were carefully reviewed and selected from 110 submissions. There was a co-organized workshop on computational social networks (CSoNet 2014) where 8 papers were accepted. The papers cover the following topics: sampling and randomized methods; logic, algebra and automata; database and data structures; parameterized complexity and algorithms; computational complexity; computational biology and computational geometry; approximation algorithm; graph theory and algorithms; game theory and cryptography; scheduling algorithms and circuit complexity and CSoNet.

Fundamentals of Computation Theory

20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings

Author: Adrian Kosowski,Igor Walukiewicz

Publisher: Springer

ISBN: 3319221779

Category: Computers

Page: 395

View: 8574

This book constitutes the refereed proceedings of the 20th International Symposium on Fundamentals of Computation Theory, FCT 2015, held in Gdańsk, Poland, in August 2015. The 27 revised full papers presented were carefully reviewed and selected from 60 submissions. The papers cover topics in three main areas: algorithms, formal methods, and emerging fields and are organized in topical sections on geometry, combinatorics, text algorithms; complexity and Boolean functions; languages; set algorithms, covering, and traversal; graph algorithms and networking applications; anonymity and indistinguishability; graphs, automata, and dynamics; and logic and games.

Complexity and Approximation

Combinatorial Optimization Problems and Their Approximability Properties

Author: Giorgio Ausiello,Pierluigi Crescenzi,Giorgio Gambosi,Viggo Kann,Alberto Marchetti-Spaccamela,Marco Protasi

Publisher: Springer Science & Business Media

ISBN: 3642584128

Category: Computers

Page: 524

View: 9496

This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.

Randomized Algorithms

Author: Rajeev Motwani,Prabhakar Raghavan

Publisher: Cambridge University Press

ISBN: 1139643134

Category: Computers

Page: N.A

View: 947

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.

Descriptional Complexity of Formal Systems

16th International Workshop, DCFS 2014, Turku, Finland, August 5-8, 2014, Proceedings

Author: Helmut Jürgensen,Juhani Karhumäki,Alexander Okhotin

Publisher: Springer

ISBN: 3319097040

Category: Computers

Page: 366

View: 2898

This book constitutes the refereed proceedings of the 16th International Conference on Descriptional Complexity of Formal Systems, DCFS 2014, held in Turku, Finland, in August 2014. The 27 full papers presented were carefully reviewed and selected from 35 submissions. The conference dealt with the following topics: Automata, grammars, languages and other formal systems; various modes of operation and complexity measures; trade-offs between computational models and modes of operation; succinctness of description of objects, state explosion-like phenomena; circuit complexity of Boolean functions and related measures; resource-bounded or structure-bounded environments; frontiers between decidability and undecidability; universality and reversibility; structural complexity; formal systems for applications (e.g., software reliability, software and hardware testing, modeling of natural languages); nature-motivated (bio-inspired) architectures and unconventional models of computing; complexity aspects of combinatorics on words; Kolmogorov complexity.

Analysis of Boolean Functions

Author: Ryan O'Donnell

Publisher: Cambridge University Press

ISBN: 1107038324

Category: Computers

Page: 444

View: 7094

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Computer Vision

Algorithms and Applications

Author: Richard Szeliski

Publisher: Springer

ISBN: 9781848829466

Category: Computers

Page: 812

View: 4428

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Algorithmic Aspects of Parallel Data Processing

Author: Paraschos Koutris,Semih Salihoglu,Dan Suciu

Publisher: N.A

ISBN: 9781680834062

Category: Computers

Page: 144

View: 4229

This monograph reviews some of the recent theoretical results on efficient data processing on large distributed architectures, as well as some of the relevant classical results on parallel sorting and parallel matrix multiplication.

Algorithms and Data Structures in VLSI Design

OBDD - Foundations and Applications

Author: Christoph Meinel,Thorsten Theobald

Publisher: Springer Science & Business Media

ISBN: 3642589405

Category: Computers

Page: 268

View: 7987

One of the main problems in chip design is the enormous number of possible combinations of individual chip elements within a system, and the problem of their compatibility. The recent application of data structures, efficient algorithms, and ordered binary decision diagrams (OBDDs) has proven vital in designing the computer chips of tomorrow. This book provides an introduction to the foundations of this interdisciplinary research area, emphasizing its applications in computer aided circuit design.

Pattern Recognition with Fuzzy Objective Function Algorithms

Author: James C. Bezdek

Publisher: Springer Science & Business Media

ISBN: 147570450X

Category: Mathematics

Page: 272

View: 7273

The fuzzy set was conceived as a result of an attempt to come to grips with the problem of pattern recognition in the context of imprecisely defined categories. In such cases, the belonging of an object to a class is a matter of degree, as is the question of whether or not a group of objects form a cluster. A pioneering application of the theory of fuzzy sets to cluster analysis was made in 1969 by Ruspini. It was not until 1973, however, when the appearance of the work by Dunn and Bezdek on the Fuzzy ISODATA (or fuzzy c-means) algorithms became a landmark in the theory of cluster analysis, that the relevance of the theory of fuzzy sets to cluster analysis and pattern recognition became clearly established. Since then, the theory of fuzzy clustering has developed rapidly and fruitfully, with the author of the present monograph contributing a major share of what we know today. In their seminal work, Bezdek and Dunn have introduced the basic idea of determining the fuzzy clusters by minimizing an appropriately defined functional, and have derived iterative algorithms for computing the membership functions for the clusters in question. The important issue of convergence of such algorithms has become much better understood as a result of recent work which is described in the monograph.

An Introduction to the Analysis of Algorithms

Author: Robert Sedgewick,Philippe Flajolet

Publisher: Addison-Wesley

ISBN: 0133373487

Category: Computers

Page: 604

View: 1011

Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field. Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance. Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure. Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s The Art of Computer Programming books—and provide the background they need to keep abreast of new research. "[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways." —From the Foreword by Donald E. Knuth

Algorithmic Graph Theory and Perfect Graphs

Author: Martin Charles Golumbic

Publisher: Elsevier

ISBN: 1483271978

Category: Mathematics

Page: 306

View: 6510

Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.

Algorithm Design: Pearson New International Edition

Author: Jon Kleinberg,Eva Tardos

Publisher: Pearson Higher Ed

ISBN: 1292037040

Category: Computers

Page: 832

View: 2323

August 6, 2009 Author, Jon Kleinberg, was recently cited in the New York Times for his statistical analysis research in the Internet age. Algorithm Design introduces algorithms by looking at the real-world problems that motivate them. The book teaches students a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science.

A Course in Enumeration

Author: Martin Aigner

Publisher: Springer Science & Business Media

ISBN: 3540390359

Category: Mathematics

Page: 565

View: 5575

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

Combinatorial Algorithms

Theory and Practice

Author: Edward Martin Reingold,J urg Nievergelt,N. Deo

Publisher: Prentice Hall


Category: Mathematics

Page: 433

View: 8964