Randomized Algorithms

  • Filename: randomized-algorithms.
  • ISBN: 0521474655
  • Release Date: 1995-08-25
  • Number of pages: 476
  • Author: Rajeev Motwani
  • Publisher: Cambridge University Press



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.

Probability and Computing

  • Filename: probability-and-computing.
  • ISBN: 0521835402
  • Release Date: 2005-01-31
  • Number of pages: 352
  • Author: Michael Mitzenmacher
  • Publisher: Cambridge University Press



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.

Randomized Algorithms for Analysis and Control of Uncertain Systems

  • Filename: randomized-algorithms-for-analysis-and-control-of-uncertain-systems.
  • ISBN: 9781447146100
  • Release Date: 2012-10-21
  • Number of pages: 360
  • Author: Roberto Tempo
  • Publisher: Springer Science & Business Media



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

Randomized Algorithms

  • Filename: randomized-algorithms.
  • ISBN: 9781139643139
  • Release Date: 1995-08-25
  • Number of pages:
  • Author: Rajeev Motwani
  • Publisher: Cambridge University Press



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.

Concentration of Measure for the Analysis of Randomized Algorithms

  • Filename: concentration-of-measure-for-the-analysis-of-randomized-algorithms.
  • ISBN: 9781139480994
  • Release Date: 2009-06-15
  • Number of pages:
  • Author: Devdatt P. Dubhashi
  • Publisher: Cambridge University Press



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.

Computational Geometry

  • Filename: computational-geometry.
  • ISBN: STANFORD:36105003459646
  • Release Date: 1994
  • Number of pages: 447
  • Author: Ketan Mulmuley
  • Publisher: Prentice Hall



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.

Primality Testing in Polynomial Time

  • Filename: primality-testing-in-polynomial-time.
  • ISBN: 9783540403449
  • Release Date: 2004-06-29
  • Number of pages: 147
  • Author: Martin Dietzfelbinger
  • Publisher: Springer Science & Business Media



On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the “primality problem”hasa“deterministic algorithm” that runs in “polynomial time”. Finding out whether a given number n is a prime or not is a problem that was formulated in ancient times, and has caught the interest of mathema- ciansagainandagainfor centuries. Onlyinthe 20thcentury,with theadvent of cryptographic systems that actually used large prime numbers, did it turn out to be of practical importance to be able to distinguish prime numbers and composite numbers of signi?cant size. Readily, algorithms were provided that solved the problem very e?ciently and satisfactorily for all practical purposes, and provably enjoyed a time bound polynomial in the number of digits needed to write down the input number n. The only drawback of these algorithms is that they use “randomization” — that means the computer that carries out the algorithm performs random experiments, and there is a slight chance that the outcome might be wrong, or that the running time might not be polynomial. To ?nd an algorithmthat gets by without rand- ness, solves the problem error-free, and has polynomial running time had been an eminent open problem in complexity theory for decades when the paper by Agrawal, Kayal, and Saxena hit the web.

Design and Analysis of Randomized Algorithms

  • Filename: design-and-analysis-of-randomized-algorithms.
  • ISBN: 3540239499
  • Release Date: 2005-06-14
  • Number of pages: 277
  • Author: J. Hromkovic
  • Publisher: Springer Science & Business Media



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

Design and Analysis of Randomized Algorithms

  • Filename: design-and-analysis-of-randomized-algorithms.
  • ISBN: 9783540279037
  • Release Date: 2006-03-30
  • Number of pages: 277
  • Author: J. Hromkovic
  • Publisher: Springer Science & Business Media



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

Randomized Algorithms in Automatic Control and Data Mining

  • Filename: randomized-algorithms-in-automatic-control-and-data-mining.
  • ISBN: 9783642547867
  • Release Date: 2014-07-14
  • Number of pages: 251
  • Author: Oleg Granichin
  • Publisher: Springer



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.

Robust Computation of Aggregates in Wireless Sensor Networks Distributed Randomized Algorithms and Analyses

  • Filename: robust-computation-of-aggregates-in-wireless-sensor-networks-distributed-randomized-algorithms-and-analyses.
  • ISBN: 9780549563549
  • Release Date: 2007
  • Number of pages: 147
  • Author:
  • Publisher: ProQuest



A wireless sensor network consists of a large number of small, resource-constrained devices and usually operates in a hostile environment that is prone to link and node failures. Consequently, the algorithms developed on a sensor network have to be prudent on energy cost, scalable to network size, and robust to frequent topology changes. Among the operations on a sensor network, computing aggregates such as average, minimum, maximum and sum over the data stored in the sensor nodes is not only an important application in itself but also fundamental to various other functions such as system monitoring, data querying, and collaborative information processing. In this work, we present a class of distributed randomized algorithms to efficiently compute aggregates in a sensor network. The proposed algorithms are energy-efficient, scalable, and robust to frequent topology changes. Our analyses and experimental results show that they outperform other representative distributed algorithms for the aggregates computation in wireless sensor networks.

An Introduction to Bioinformatics Algorithms

  • Filename: an-introduction-to-bioinformatics-algorithms.
  • ISBN: 0262101068
  • Release Date: 2004
  • Number of pages: 435
  • Author: Neil C. Jones
  • Publisher: MIT Press



An introductory text that emphasizes the underlying algorithmic ideas that are driving advances in bioinformatics.

Adaptive Randomized Algorithms for Validation and Analysis of Complex Systems

  • Filename: adaptive-randomized-algorithms-for-validation-and-analysis-of-complex-systems.
  • ISBN: 0542799162
  • Release Date: 2006
  • Number of pages: 140
  • Author:
  • Publisher: ProQuest



This thesis addresses the problem of validating software-enabled controllers for complex systems with dynamic constraints. In such complex systems, the controllers cannot be designed with performance guarantees. Analytical methods for analysis fail because the computation of the reachable set for a given set of initial conditions is intractable. Thus, it is necessary to establish and verify performance using simulation techniques. This is particularly true in hybrid systems where the control algorithms often involve a switching between different controllers. While it is possible to analyze simple systems and each controller in isolation, there is no systematic approach to testing and validating the complex continuous and hybrid systems.

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