Randomized Algorithms
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| Author | : Rajeev Motwani |
| Publisher | : Cambridge University Press |
| Total Pages | : 496 |
| Release | : 1995-08-25 |
| Genre | : Computers |
| ISBN | : 1139643134 |
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.
| Author | : Michael Mitzenmacher |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 2005-01-31 |
| Genre | : Computers |
| ISBN | : 9780521835404 |
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. This 2005 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. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
| Author | : Devdatt P. Dubhashi |
| Publisher | : Cambridge University Press |
| Total Pages | : 213 |
| Release | : 2009-06-15 |
| Genre | : Computers |
| ISBN | : 1139480995 |
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.
| Author | : J. Hromkovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2005-10-11 |
| Genre | : Computers |
| ISBN | : 3540279032 |
Systematically teaches key paradigmic algorithm design methods Provides a deep insight into randomization
| Author | : Roberto Tempo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2012-10-21 |
| Genre | : Technology & Engineering |
| ISBN | : 1447146107 |
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
| Author | : Oleg Granichin |
| Publisher | : Springer |
| Total Pages | : 268 |
| Release | : 2014-07-14 |
| Genre | : Technology & Engineering |
| ISBN | : 3642547869 |
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.
| Author | : A. Sinclair |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 161 |
| Release | : 1993-02 |
| Genre | : Computers |
| ISBN | : 0817636587 |
This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.
| Author | : Ketan Mulmuley |
| Publisher | : Prentice Hall |
| Total Pages | : 472 |
| Release | : 1994 |
| Genre | : Computers |
| ISBN | : |
For beginning graduate-level courses in computational geometry. This up-to-date and concise introduction to computational geometry with emphasis on simple randomized methods is designed for quick, easy access to beginners.
| Author | : Dr. PKS Prakash |
| Publisher | : Packt Publishing Ltd |
| Total Pages | : 266 |
| Release | : 2016-11-21 |
| Genre | : Computers |
| ISBN | : 1786464160 |
Increase speed and performance of your applications with efficient data structures and algorithms About This Book See how to use data structures such as arrays, stacks, trees, lists, and graphs through real-world examples Find out about important and advanced data structures such as searching and sorting algorithms Understand important concepts such as big-o notation, dynamic programming, and functional data structured Who This Book Is For This book is for R developers who want to use data structures efficiently. Basic knowledge of R is expected. What You Will Learn Understand the rationality behind data structures and algorithms Understand computation evaluation of a program featuring asymptotic and empirical algorithm analysis Get to know the fundamentals of arrays and linked-based data structures Analyze types of sorting algorithms Search algorithms along with hashing Understand linear and tree-based indexing Be able to implement a graph including topological sort, shortest path problem, and Prim's algorithm Understand dynamic programming (Knapsack) and randomized algorithms In Detail In this book, we cover not only classical data structures, but also functional data structures. We begin by answering the fundamental question: why data structures? We then move on to cover the relationship between data structures and algorithms, followed by an analysis and evaluation of algorithms. We introduce the fundamentals of data structures, such as lists, stacks, queues, and dictionaries, using real-world examples. We also cover topics such as indexing, sorting, and searching in depth. Later on, you will be exposed to advanced topics such as graph data structures, dynamic programming, and randomized algorithms. You will come to appreciate the intricacies of high performance and scalable programming using R. We also cover special R data structures such as vectors, data frames, and atomic vectors. With this easy-to-read book, you will be able to understand the power of linked lists, double linked lists, and circular linked lists. We will also explore the application of binary search and will go in depth into sorting algorithms such as bubble sort, selection sort, insertion sort, and merge sort. Style and approach This easy-to-read book with its fast-paced nature will improve the productivity of an R programmer and improve the performance of R applications. It is packed with real-world examples.
| Author | : James Aspnes |
| Publisher | : |
| Total Pages | : 354 |
| Release | : 2014-12-05 |
| Genre | : |
| ISBN | : 9781505381474 |
Notes on Randomized AlgorithmsBy James Aspnes
