Randomized Algorithms

Author: Rajeev Motwani,Prabhakar Raghavan

Publisher: Cambridge University Press

ISBN: 9780521474658

Category: Computers

Page: 476

View: 2133

For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

Randomized Algorithms: Approximation, Generation, and Counting

Author: Russ Bubley

Publisher: Springer Science & Business Media

ISBN: 1447106954

Category: Computers

Page: 152

View: 5525

Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.

Probability and Computing

Randomized Algorithms and Probabilistic Analysis

Author: Michael Mitzenmacher,Eli Upfal

Publisher: Cambridge University Press

ISBN: 9780521835404

Category: Computers

Page: 352

View: 1668

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols.Assuming only an elementary background in discrete mathematics, this textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses, including random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics.

Concentration of Measure for the Analysis of Randomized Algorithms

Author: Devdatt P. Dubhashi,Alessandro Panconesi

Publisher: Cambridge University Press

ISBN: 1139480995

Category: Computers

Page: N.A

View: 8138

Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff–Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff–Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

Design and Analysis of Randomized Algorithms

Introduction to Design Paradigms

Author: J. Hromkovic

Publisher: Springer Science & Business Media

ISBN: 3540279032

Category: Computers

Page: 277

View: 8787

Systematically teaches key paradigmic algorithm design methods Provides a deep insight into randomization

Randomized Algorithms for Analysis and Control of Uncertain Systems

With Applications

Author: Roberto Tempo,Giuseppe Calafiore,Fabrizio Dabbene

Publisher: Springer Science & Business Media

ISBN: 1447146107

Category: Technology & Engineering

Page: 360

View: 4406

The presence of uncertainty in a system description has always been a critical issue in control. The main objective of Randomized Algorithms for Analysis and Control of Uncertain Systems, with Applications (Second Edition) is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of systems subject to deterministic and stochastic uncertainty. The approach propounded by this text guarantees a reduction in the computational complexity of classical control algorithms and in the conservativeness of standard robust control techniques. The second edition has been thoroughly updated to reflect recent research and new applications with chapters on statistical learning theory, sequential methods for control and the scenario approach being completely rewritten. Features: · self-contained treatment explaining Monte Carlo and Las Vegas randomized algorithms from their genesis in the principles of probability theory to their use for system analysis; · development of a novel paradigm for (convex and nonconvex) controller synthesis in the presence of uncertainty and in the context of randomized algorithms; · comprehensive treatment of multivariate sample generation techniques, including consideration of the difficulties involved in obtaining identically and independently distributed samples; · applications of randomized algorithms in various endeavours, such as PageRank computation for the Google Web search engine, unmanned aerial vehicle design (both new in the second edition), congestion control of high-speed communications networks and stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems (second edition) is certain to interest academic researchers and graduate control students working in probabilistic, robust or optimal control methods and control engineers dealing with system uncertainties. The present book is a very timely contribution to the literature. I have no hesitation in asserting that it will remain a widely cited reference work for many years. M. Vidyasagar

Primality Testing in Polynomial Time

From Randomized Algorithms to "PRIMES Is in P"

Author: Martin Dietzfelbinger

Publisher: Springer Science & Business Media

ISBN: 3540403442

Category: Mathematics

Page: 150

View: 6735

A self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal and Saxena. The volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.

Randomized Algorithms in Automatic Control and Data Mining

Author: Oleg Granichin,Zeev (Vladimir) Volkovich,Dvora Toledano-Kitai

Publisher: Springer

ISBN: 3642547869

Category: Computers

Page: 251

View: 6247

In the fields of data mining and control, the huge amount of unstructured data and the presence of uncertainty in system descriptions have always been critical issues. The book Randomized Algorithms in Automatic Control and Data Mining introduces the readers to the fundamentals of randomized algorithm applications in data mining (especially clustering) and in automatic control synthesis. The methods proposed in this book guarantee that the computational complexity of classical algorithms and the conservativeness of standard robust control techniques will be reduced. It is shown that when a problem requires "brute force" in selecting among options, algorithms based on random selection of alternatives offer good results with certain probability for a restricted time and significantly reduce the volume of operations.

Computational Geometry

An Introduction Through Randomized Algorithms

Author: Ketan Mulmuley

Publisher: Prentice Hall


Category: Computers

Page: 447

View: 1708

This introduction to computational geometry is designed for beginners. It emphasizes simple randomized methods, developing basic principles with the help of planar applications, beginning with deterministic algorithms and shifting to randomized algorithms as the problems become more complex. It also explores higher dimensional advanced applications and provides exercises.

An Introduction to Bioinformatics Algorithms

Author: Neil C. Jones,Pavel A. Pevzner,Pavel Pevzner

Publisher: MIT Press

ISBN: 9780262101066

Category: Computers

Page: 435

View: 8686

Algorithms and Complexity. Molecular Biology Primer. Exhaustive Search. Greedy Algorithms. Dynamic Programming Algorithms. Divide-and-Conquer Algorithms. Graph Algorithms. Combinatorial Pattern Matching. Clustering and Trees. Hidden Markov Models. Randomized Algorithms.

Randomized Algorithms for Matrices and Data

Author: Michael W. Mahoney

Publisher: N.A

ISBN: 9781601985064

Category: Computers

Page: 114

View: 7100

Randomized Algorithms for Matrices and Data provides a detailed overview, appropriate for both students and researchers from all of these areas, of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis

Handbook of Randomized Computing

Author: Sanguthevar Rajasekaran

Publisher: Springer Science & Business Media

ISBN: 9780792369585

Category: Computers

Page: 941

View: 8165

Towards Dynamic Randomized Algorithms in Computational Geometry

Author: Monique Teillaud

Publisher: Springer

ISBN: 9783540482024

Category: Computers

Page: 169

View: 9774

Computational geometry concerns itself with designing and analyzing algorithms for solving geometric problems. The field has reached a high level of sophistication, and very complicated algorithms have been designed.However, it is also useful to develop more practical algorithms, so long as they are based on rigorous methods. One such method is the use of randomized algorithms. These algorithms have become more and more popular, turning into one of the hottest areas of recent years. Dynamic algorithms are particularly interesting because in practice the data of a problem are often acquired progressively. In this monograph the author studies the theoretical complexity and practical efficiency of randomized dynamic algorithms.

Introduction To Algorithms

Author: Thomas H.. Cormen,Thomas H Cormen,Charles E Leiserson,Ronald L Rivest,Clifford Stein

Publisher: MIT Press

ISBN: 9780262032933

Category: Computers

Page: 1180

View: 3257

An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms.

Randomized Algorithms for Graph Problems with Incomplete Information

Author: Xiaowei Wu

Publisher: N.A

ISBN: 9781361009062


Page: N.A

View: 3425

This dissertation, "Randomized Algorithms for Graph Problems With Incomplete Information" by Xiaowei, Wu, 吴晓伟, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: I study several graph problems in which the information of the given graphs are incomplete. I devise randomized algorithms to solve those problems and provide theoretical analysis for their performances. In the rumor spreading problem, a connected graph with n nodes is given and the objective is to spread a rumor, which is initiated by one node, to all nodes in the graph as fast as possible under distributed communication. I extend the classic PUSH-PULL protocol to stream B rumors in a graph from a single source node to all nodes in the graph and show that perfect pipelining can be achieved with high probability in directed random graphs and PA-graphs. Motivated by online advertisement and exchange settings, the oblivious matching problem aims at finding a maximum matching between nodes in a simple undirected graph whose edges are oblivious to the algorithm. An algorithm for the problem determines an ordering of all unordered pairs of nodes and tries to match the pairs greedily according to the ordering. While any greedy algorithm for the problem has performance ratio at least 0:5, no algorithm achieves performance ratio strictly above 0:5 until Aronson et al. proved that the Modified Randomized Greedy algorithm achieves a performance ratio 0:5 + 1/400000 on arbitrary graphs. I revisit the classic Ranking algorithm for the problem and derive a linear program, whose optimal solution provides a lower bound for the performance ratio, by analyzing the structural properties of the Ranking algorithm. I show that the Ranking algorithm has a performance ratio at least 0:523166, which is the optimal solution for our linear program. I later improve the performance ratio to 0:526823 by exploring more sophisticated properties of the Ranking algorithm. In the node-weighted version of the oblivious matching problem, each node of the graph has a non-negative weight and the objective is to form a matching that maximizes the total weight of matched nodes. I provide a weighted version of the Ranking algorithm for this problem and show that its performance ratio is at least 0:501505, which is the first non-trivial performance ratio strictly above 0:5 for the node-weighted version of the problem. Subjects: Graph theory - Data processing Stochastic processes - Data processing Algorithms

Algorithmen - Eine Einführung

Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110522012

Category: Computers

Page: 1339

View: 604

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.