Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Book Description

Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes 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. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.

Customer Reviews:

Advanced probability topics without measure theory.......2007-08-18

This book is underestimated by two reviewers below. I totally do not agree with them. This book covers a wide range of topics in a very readable style. The contents in this book is complementary to the book of Motwani and Raghavan (but this book is much easier to digest).

It, without requiring any knowledge on measure theory, contains excellent introductions to many difficult topics in probability including

- concentration bounds (Chernoff, Azuma-Hoeffding, etc.)
- applications of stochastic processes such as queuing theory
- martingale (Wald's equation)
- coupling of Markov chains and their mixing times
- Shannon's source coding and noisy channel theorems
- Erdos' probabilistic method
- etc.

All of these topics are provided with excellent applications in computing.
The authors illustrate many clever tricks for proving theorems, and these tricks give insights to the readers as well.

Just unnecessary.......2007-05-17

This book, while written by two renowned computer scientists, is truly disappointing. In trying to discuss randomness and computation, this book just does a mediocre job on discussing randomized computation and also an equally poor job discussing relevant aspects of probability theory. Their approach is not novel and many of their examples can be found in other texts. If you really want to learn randomized computation, get Motwani et al's book on Randomized Algorithms. If you want to learn probability theory, get any advanced probability theory book like Spencer and Alon on the probabilistic method, one of Sheldon Ross's books, or even Grimmett and Stirzaker. Whatever you do don't get this weak hybrid of a book that will require you to get another book at some point to supplement your understanding.

Another poorly written text book.......2006-03-19

The authors must be smart guys. They obviously understand alot about this subject but make the mistake that you do too! As a result, the book is inadequate as a teaching tool.

They use only half to a third of the narrative they need to adequately explain a subject. They also like to leave out proof steps or not explain them. The problems at the end of chapters are poor as well, since the authors seem to have forgotten to teach the techniques needed to solve most them in the chapter they belong to.

I am sure to them it is intuitive.

Good Introductory Textbook.......2005-03-16

It's pretty easy to get computers to do things where the answer is yes or no, or 4 or 6, given that the inputs to the problem are known. It's much harder to get an answer to a problem where the answer is that their is a 62% chance that the answer is yes. Unfortunately, in real life it's this second class of problems that predominates.

This book is oriented to solving these kinds of real world problems. The exercises in the book are chosen from real world examples -- what we used to call story problems. This tends to give the student a better understanding of not only the mathematics and programming involved but experience in looking at problems with a view to understanding this approach to solving the problem.

This book is suitable for a one or two semester introductory class at the upper undergraduate or beginning graduate level.

Just a word about the illustration on the front of the book. At the end of the book Alice in Wonderland the queen is about to order Alice beheaded. Alice says, "You're nothing but a pack of cards." At this, the whole pack rose up into the air and came flying down around her. This illustration is by John Tenniel from the original book of 1899. A deck of flying playing cards is a good way to illustrate random and probability.

Average customer rating:

Book that didn't meet my expectations
More work should be done in proofs
A subtle introduction to probablistic algoritms
An enciclopedia for randomized algorithms.
extremely informative but obscure

Randomized Algorithms
Rajeev Motwani , and Prabhakar Raghavan
Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521474655

Book Description

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.

Customer Reviews:

Book that didn't meet my expectations.......2006-09-18

Algorithms are my specialty, and I'm really interest in everything that is connected with them. This is one of the few books from the field of algorithms that I was a problem to read. I found this book hard to read because of several reasons.

Firstly, i have a problem with the composition of material from the book. The material is in the many places presented in the unnatural way. Book is method oriented, so often same problem is treated in several places in the book. On the other hand the book is not fully method oriented, so there are chapters of the book that don't present any method of building randomized algorithms. There are several chapters that are organized around some concept from the probability theory. I don't see the reason for these two orientation to be mixed.

Often I have a feeling that authors are not particulary interested in randomized algorithms, and that thet their main interest is to show probability methods in the theory of algorithms. So, there are, for example, chapters in the book named "Moments and Deviations" and "Tail Inequalities". I don't want to say that these concepts are not important for the randomized algorithm complexity claculations, but I think that such chapters belongs to book on probability theory, not randomized algorithms book. On the other side, therms of Monte Carlo and Las Vegas algorithms get together one section in the chapter in which they are described. It is true that in these chapters contain randomized algorithms as examples of usage of mathematical concepts, but the question is: should this book present general mathematical concepts, or randomized algorithms.

The second big drawback is lack of precise mathematical notion in many places in the book. For example, in the chapter on game theory the reader get impression that the whole game theory are game trees. Yet, authors fail to define what game tree is. The definition they give is more lausy desciption than definition. They don't say which kind of tree is game tree. Is it binary? Of course it is not, but authors in this section work only with binary trees. Further, in the text authors said that this tree is uniform. I have to admit that I never heard about uniform trees. The problem is that all definitions in the book is given in this way, by the paragraph of the text, which describe the term, not define it. In fact, the only concepts that are properly defined are ones form the probability theory. None of the concepts from the algorithms theory or data structures theory is not defined as it should be.

The third great problem with the book is that these concepts are never ilustrated with the concrete example. There is a section about the game trees, for example, but there is no single game tree for some game generated in this section. This is not a single case. All examples in the book are about mathmatical, or nore precisely probability theory concepts, and all of them looks like they are taken from the workbook on probability theory, and doesn't have any connection with algorithms.

Another problem is that all chapters are not builded in the same manner. There are chapters (unfortenately very little of them) that have theoretical overview of the method they deal with, but in the other chapters there are no proper theoretical description of the method of the matter.

To resume, this book shows the lack of concept and system in the writting, as well as the interest of authors more in mathmatics than in algorithm field.

My opinion is that there are much better books on the randomized algorithms tnan this one.

More work should be done in proofs.......2004-11-02

Overall, the authors explain core concepts, the examples and the possible applications well. However, the readibility of their proof is far from that of the above three. Honestly some proofs should be re-written completely.

For example, in page 116, they try to use the induction method to prove Lova(')sz Local Lemma. After reading that page many times, I still didn't understand the structure of their proof.

I was TA for under-grad level algorithm course, got A+ in advanced Calculus II and A in intro. to PDE (both in under-grad level), really knew something about induction method and a little bit about algorithm. I am not smart, but far from stupid.

In the end, I google the internet and found a 3-page proof for the same thing. That's easy to catch in few minutes, and then, I understand the 1-page proof in the book. Is it ironic?

A subtle introduction to probablistic algoritms.......2002-01-14

This book is a jewel. It demonstrates how clever and beautifully simple probabilistic ideas can lead to the design of very efficient algorithms. I like its very verbal intuitive style,
with proof strategies being always transparently explained.
For computer scientists, this is *the* reference work in randomized algorithms, by now a major paradigm of algorithms design. For classical probabilists, this
could serve as an eye-opener on unsuspected applications of their field to important areas of computer science.

An enciclopedia for randomized algorithms........2001-07-21

The book has an exoustive amount of algorithms. Not everything is proved. Sometimes the proof contains to few steps to be understood. There are many algorithms explained well. After reading this book it is easy to create your own randomized algorithms.

extremely informative but obscure.......1999-10-16

I've taken two CS classes that use this book and I always felt like this book was very informative. The algorithms and concepts that Motwani brings forth are extremely insightful and interesting. However, the presentation of the proofs has a lot of room for improvement. Notation is carried over from previous chapters and is sometimes unexplained, which makes it very difficult for someone who does not have a lot of familiarity with the material presented. The book presents very interesting topics and leaves a lot of open (unresolved) questions to the reader's curiosity and challenge.

Randomized Algorithms for Analysis and Control of Uncertain Systems (Communications and Control Engineering)

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Randomized Algorithms for Analysis and Control of Uncertain Systems (Communications and Control Engineering)
Roberto Tempo , Giuseppe Calafiore , and Fabrizio Dabbene
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1852335246

Book Description

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called "randomized algorithms", this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H-infinity control.

Features:

• self-contained treatment explaining randomized algorithms from their genesis in the principles of probability theory to their use for robust analysis and controller synthesis;

• comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining independent and identically distributed samples;

• applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems.

Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all 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

Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms (Texts in Theoretical Computer Science. An EATCS Series)

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Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms (Texts in Theoretical Computer Science. An EATCS Series)
J. Hromkovic
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540239499

Book Description

Randomness is a powerful phenomenon that can be harnessed to solve various problems in all areas of computer science. Randomized algorithms are often more efficient, simpler and, surprisingly, also more reliable than their deterministic counterparts. Computing tasks exist that require billions of years of computer work when solved using the fastest known deterministic algorithms, but they can be solved using randomized algorithms in a few minutes with negligible error probabilities.

Introducing the fascinating world of randomness, this book systematically teaches the main algorithm design paradigms – foiling an adversary, abundance of witnesses, fingerprinting, amplification, and random sampling, etc. – while also providing a deep insight into the nature of success in randomization. Taking sufficient time to present motivations and to develop the reader's intuition, while being rigorous throughout, this text is a very effective and efficient introduction to this exciting field.

Primality Testing in Polynomial Time: From Randomized Algorithms to "PRIMES Is in P" (Lecture Notes in Computer Science)

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Primality Testing in Polynomial Time: From Randomized Algorithms to "PRIMES Is in P" (Lecture Notes in Computer Science)
Martin Dietzfelbinger
Manufacturer: Springer
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ASIN: 3540403442

Book Description

This book is devoted to algorithms for the venerable primality problem: Given a natural number n, decide whether it is prime or composite.

The problem is basic in number theory, efficient algorithms that solve it, i.e., algorithms that run in a number of computational steps which is polynomial in the number of digits needed to write n, are important for theoretical computer science and for applications in algorithmics and cryptology.

This book gives a self-contained account of theoretically and practically important efficient algorithms for the primality problem, covering 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 textbook is written for students of computer science, in particular for 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.

Computational Geometry: An Introduction Through Randomized Algorithms

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Poor Textbook
very good if a little specialized

Computational Geometry: An Introduction Through Randomized Algorithms
Ketan Mulmuley
Manufacturer: Prentice Hall
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Binding: Paperback

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ASIN: 0133363635

Customer Reviews:

Poor Textbook.......2003-10-25

This book is not suitable for beginners.It doesn't explain some important theorems and rules clearly,especially for "history" data structues , my classmates also can't understand how to implement it in detail ! All materials of this book seems uilding on auther's personal imaging !

very good if a little specialized.......1998-10-22

An in-depth look at randomized incremental algorithms in computational geometry. Since this appears to be the most successful and practical approach for classic problems like convex hull, Voronoi diagram and polygon triangulation, this would be a good book to own if you own just one. Especially if you are interested in theory.

Lectures on Proof Verification and Approximation Algorithms (Lecture Notes in Computer Science)

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Lectures on Proof Verification and Approximation Algorithms (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540642013

Book Description

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.

Advances in Randomized Parallel Computing (Combinatorial Optimization)

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Advances in Randomized Parallel Computing (Combinatorial Optimization)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0792357140

Book Description

The technique of randomization has become very prevalent since it offers superior performance and simplicity. Numerous researchers work in this area of vital importance. Parallel Computing is also very important since one can get excellent speedups using parallel computers. This book combines these two domains. It provides a summary of the state-of-the-art results and techniques in the area of randomized parallel computing. There are few texts in the area of randomized computing, and more surprisingly there is no text in the area of randomized parallel computing. Thus our book fills the void in this very important area.
Audience: This is a reference book for researchers, educators, and students. It can also be used as a text for an advanced graduate course on randomized computing, parallel computing, or distributed computing.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 9th International Workshop on Approximation Algorithms for Combinatorial ... (Lecture Notes in Computer Science)

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 9th International Workshop on Approximation Algorithms for Combinatorial ... (Lecture Notes in Computer Science)

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Book Description

This book constitutes the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006, held in Barcelona, Spain, in August 2006.

The 44 revised full papers presented were carefully reviewed and selected from 105 submissions. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, game theory, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness, derandomization, random combinatorial structures, Markov chains, prohabalistic proof systems, error-correcting codes, etc.

Integer Optimization by Local Search: A Domain-Independent Approach (Lecture Notes in Computer Science)

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Integer Optimization by Local Search: A Domain-Independent Approach (Lecture Notes in Computer Science)
Joachim P. Walser
Manufacturer: Springer
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Binding: Paperback

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ASIN: 3540663673

Book Description

Integer Optimization addresses a wide spectrum of practically important optimization problems and represents a major challenge for algorithmics. The goal of integer optimization is to solve a system of constraints and optimization criteria over discrete variables.Integer Optimization by Local Search introduces a new approach to domain-independent integer optimization, which, unlike traditional strategies, is based on local search. It develops the central concepts and strategies of integer local search and describes possible combinations with classical methods from linear programming. The surprising effectiveness of the approach is demonstrated in a variety of case studies on large-scale, realistic problems, including production planning, timetabling, radar surveillance, and sports scheduling. The monograph is written for practitioners and researchers from artificial intelligence and operations research.

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