Book Description

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach.

Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks. . . it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs."

Presenting powerful, proven optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems.

Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. ... Read more

Book Description

In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students. ... Read more

Reviews (3)

Graduate Level Text
This is a good reference text for the fundamentals, It is used at the Georgia Institute of Technology for a graduate math class.

Amazon is slow
Amazon can't get copies of this book so don't even try ordering it from them. They said they ordered this title from the publisher twelve weeks ago and told me I would have it in 4-6 weeks

general linear model
estimation in the full rank model hypothesis testing in the full rank model estimation in the less than full rank model hypothesis testing in the less than full rank model ... Read more

Book Description

Modeling and simulation are central to a mechanical engineer's activity. Increasingly complex models are being used routinely on a daily basis. This revolution is the result of the extraordinary progress in computer technology in terms of both hardware and software. This work deals with the control of the hypotheses leading from a mechanical model, usually coming from continuum mechanics, to a numerical model, i.e. the mastery of the mechanical computation process itself.  Particular attention is given to structural analysis which, in this context, is the most advanced domain. A significant part of this work is dedicated to the application of error estimators to the control of the various parameters involved in a calculation, beginning with the parameters related to the mesh. ... Read more

Book Description

Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences.

The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely. By providing the necessary proofs and presenting the material in a conversational style, Franklin made Methods of Mathematical Economics extremely popular among students. The addition of a list of errata, new to this edition, should add to the book's popularity as well as its usefulness both in the classroom and for individual study.

The book has three chapters: "Linear Programming," "Nonlinear Programming," and "Fixed-Point Theorems." The first and third chapters include the economic equilibrium theorems of von Neumann and of J. F. Nash, while the second chapter includes Kuhn-Tucker theory and Wolfe's simplex algorithm for quadratic programming. The book concludes with easy, elementary proofs of the famous theorems of Brouwer, of Kakutani, and of Schauder. These fundamental results are usually proved only in advanced texts in topology, economic theory, and nonlinear analysis.

Audience
This book is intended for undergraduate and graduate students of mathematics and economics; it requires no background in these areas except an understanding of elementary calculus and linear algebra.

Contents
Preface to the Classics Edition; Preface; Errata; Chapter 1: Linear Programming. Introduction to Linear Programming; Linear Programs and Their Duals; How the Dual Indicates Optimality; Basic Solutions; The Idea of the Simplex Methods; Separating Planes for Convex Sets; Finite Cones and the Farkas Alternative; The Duality Principle; Perturbations and Parametric Programming; The Simplex Tableau Algorithm; The Revised Simplex Algorithm; A Simplex Algorithm for Degenerate Problems; Multiobjective Linear Programming; Zero-Sum, Two-Person Games; Integer Programming: Gomory's Method; Network Flows; Assignment and Shortest-Route Problems; The Transportation Problem; Chapter 2: Nonlinear Programming. Wolfe's Method for Quadratic Programming; Kuhn-Tucker Theory; Geometric Programming; Chapter 3: Fixed-Point Theorems. Introduction to Fixed Points; Contraction Mappings; Garsia's Proof of the Brouwer Fixed-Point Theorem; Milnor's Proof of the Brouwer Fixed-Point Theorem; Barycentric Coordinates, Sperner's Lemma, and an Elementary Proof of the Brouwer Fixed-Point Theorem; The Schauder Fixed-Point Theorem; Kakutani's Fixed-Point Theorem and Nash's Theorem for n-Person Games; Index. ... Read more

Book Description

Entertaining, non-technical introduction covers basic concepts of linear programming and its relationship to operations research; geometric interpretation and problem solving, solution techniques, network problems, much more. Appendix offers precise statements of definitions, theorems, and techniques, additional computational procedures. Only high-school algebra needed. Bibliography.
... Read more

Reviews (4)

An effective introduction to Linear Programming
For someone with an interest in learning LP but not the best mathematical foundation for learning it, this book worked for me. I think the author is an experienced teacher of people with math skills such as mine and knew how present the material and explain it in familiar terms.
The book does not have all the material I need but did get me going in a confident manner so I could handle the other books I bought before I bought this one.

Great intro to Linear Programming
This book is a great non-technical introduction to a very technical subject: linear programming. If you are interested in linear programming but you don't want to all of the mathematical details, then buy this book. Hey, you can't beat the price.

By the way, how can anyone expect a book like this to tell someone how to apply linear programming. Doing that requires a lot more technical training and there are other more detailed and more expensive books that explain how to apply linear programming. This book is a great introduction a complicated subject. You will enjoy this book if your expectations are reasonable.

Good, but a reprint from 1970
This book presents a good conceptual overview of linear programming, geared for the non-mathmatical person. However, it is a reprint of a 1970 title, so there isn't much on the use of computers to solve this type of problem.

An Illustrated Guide to Linear Programming
This book is an excellent treatment of linear programming for non-technical people. It describes a number of basic business-world applications that can be readily solved using standard linear programming methods. I recommend it highly because it presents the complex principles of this important methodology in an easy-to-read manner. ... Read more

Book Description

This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics.It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way.The book contains complete (but concise) proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. From the reviews of the 2nd edition: "This book on combinatorial optimization is a beautiful example of the ideal textbook. [....] The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." J. Köhler, Halle an der Saale ELSEVIER Operations Rearch Letters, 2005, Issue 33. ... Read more

Reviews (1)

Useful yet dense!
This is the most comprehensive compilation on combinatorial optiomization I have seen so far.
Usually, Papadimitriou's book is a good place for this material - but in many cases, looking for proofs and theorems - I had to use several books:
(*) Combinatorial Optimization Algorithms and Complexity by Papadimitriou and Steiglitz.
(*) Integer and Combinatorial Optimization by Nemhauser and Wolsey
(*) Theory of linear and integer programming by Schrijver
(*) Combinatorial Optimization by Cook, Cunningham, Pulleyblank and Schrijver
(*)Combinatorial Algorithms by Kreher and Stinson

This book, on the other hand, contains so much information and so many proved theorems - it's the richest resuorce in this topic, in my humble opinion.

Using it as a graduate level textbook for an *introduction* to combinatorial optimization is kind of hard - as although it's richness, some topics are described without enough detail or examples (like the topics on network flow and bipartite graphs) - yet the authors probably assumed some previous knowledge in those topics.

I prefer using this book as a reference rather than and intoduction.

The heavy mathematical notations in this book might scare some readers, but no-fear! You quickly get used to it, and appreciate the greatness in the notations, as they make the theorems more short and to the point. On the other hand - getting back to this book for a quick review on some subject might forceyou to flip pages for a fwe minutes, just to remember the notation again.

The authors intended this book to be a graduaet level textbook or an up-to-date referencework for current research. I believe they accomplished both targets! ... Read more

Book Description

The Handbook of Metaheuristics provides both the research and practitioner communities with a comprehensive coverage of the metaheuristic methodologies that have proven to be successful in a wide variety of real-world problem settings. Moreover, it is these metaheuristic strategies that hold particular promise for success in the future. The various chapters serve as stand alone presentations giving both the necessary background underpinnings as well as practical guides for implementation. In most settings a problem solver has an option as to which metaheuristic approach should be adopted for the problem at hand. Alternative methodologies typically exist that could be employed to produce high quality solutions. Often it becomes a matter of choosing one of several approaches that could be adopted. The very nature of metaheuristics invites an analyst to modify basic methods in response to problem characteristics, past experiences, and personal preferences. The chapters in this handbook are designed to facilitate this as well.

This Handbook consists of 19 chapters. Topics covered include Scatter Search, Tabu Search, Genetic Algorithms, Genetic Programming, Memetic Algorithms, Variable Neighborhood Search, Guided Local Search, GRASP, Ant Colony Optimization, Simulated Annealing, Iterated Local Search, Multi-Start Methods, Constraint Programming, Constraint Satisfaction, Neural Network Methods for Optimization, Hyper-Heuristics, Parallel Strategies for Metaheuristics, Metaheuristic Class Libraries, and A-Teams. This family of metaheuristic chapters provides a state-of-the-art, comprehensive coverage of the major topics and methodologies of modern metaheuristics. ... Read more

Book Description

This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, and transportation problems. ... Read more

Reviews (2)

For the dedicated specialist
This book is highly mathematical. It phrases its points as a series of theorems, with a number of case studies at the end. The theorems all stop just short legible technique. The examples, though exciting, all presuppose command of technique. I regret that I never found that missing piece within myself. That piece was the one that connects deep theorems about abstract N-dimensional pseudodistances into working fluency about CAT scans.

I did, however, get some understanding of the kinds of problems that the authors address. They are some of the analytic functions, with linear or nonlinear constraints. In particular, they are functions of high dimensions - thousands or millions of constraints - amenable to fairly fine-grained optimization. They are not discrete problems, like the Travelling Salesman. They are not problems with hugely jagged reward surfaces, like "motif finding" problems in bioinformatics. They are not genetic algorithms, Monte Carlo searches, or combinatorial problems. The authors do in fact parallelize a number of important optimization problems, including CAT scans, transportation planning, and radiation therapy, but not all optimization techniques.

Those problems span only a small part of the parallelizable world. The broad promise in the title "Parallel Optimization" was only partly kept. Some parallelization techniques were presented, as well as some interesting perspetives on numerical optimization. Optimization is a large field, however, and this is only a small map.

Still, for that range of problems, it seems to offer the right reader profound insight. I can not be sure, though, since I'm not the right reader. I give it three stars, just because I had to give something. Different people will assign this book very different value.

Proximal point algorithms by Censor and Zenios
Part I of this book starts with an aphorism,
attributed to H. von Helmholtz:
``The most practical thing in the world
is a good theory.''
The book does justice to von Helmholtz maxim.
The theory of Bregman distances is presented
in a clear, geometrical and intuitive way.
Part II of the book presents several important
and illustrative applications of Proximal Point
algorithms, to constrained optimization,
Maximum Entropy problems, financial stochastic
networks, and several other important areas. ... Read more

Book Description

This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, e.g., to ordinary and partial differential operators, delay and Volterra equations and to control theory, and an emphasis on philosophical motivation and the historical background. The book is written for students, but should also be of value for researchers interested in this field. ... Read more

Reviews (2)

Outstanding Title
I guess that, besides the classic references from Pazy and Jerome Goldstein, this title outstands in its category. I've heard several words of criticism over Pazy's work due to the lack of applications and several laments over the fact that Goldstein's book is out of print. This book introduces the semigroup theory like no other: it doesn't forget the historic and philosophical aspect of subject and it's full filled with applications and deep beauty. Congrats to the authors and also to the customers that decide to buy this title, may it be PDE or Dinamic Systems, you'll be home free...

Engel et al.'s One Parameter Semigroups Book
Semigroups and Clifford algebras have become two of the main trends in mathematics and mathematical physics in the last 5 years. A researcher in either area cannot afford to be without major books and journal articles in these areas, and Engel et al.'s is the best that I have seen of recent semigroup books. Their book is a Graduate Text, but it actually presents many open questions and research ideas, as is usual for Springer and Springer-Verlag publications (and also Kluwer-Plenum and Cambridge University Press). Semigroups were familiar to those of us in probability for many years because of their Markov chain/process relationships, but the astonishing fact is that Engel et al. show that non-Markov applications and non-Hilbert space (in fact, general Banach space) applications and theorems abound. For those of us who are not too fond of Markov processes (like me), and who are also not too fond of Hilbert spaces (the usual space of Quantum Mechanics which went sour and had to be repaired by A. Bohm and still seems in bad need of repair), this is really good news. Another fascinating trend is in the direction of Positive Semigroups, which ties in with ordering results and inequalities (see my review of Clarke et al.). Positive semigroups have applications to transport and delay (differential) equations and semigroups have applications to control theory which means what it sounds like: physics-engineering control of satellites, rockets, robots, and God knows what else. I repeat my usual caution: if your background is mathematically deficient in these areas, hire a reputable consultant or tutor to translate the book into plain English more or less. If the person cannot translate in one session, look for another person, or quiz them on the phone first. ... Read more

Book Description

The first part of this book presents the essential topics for an introduction to deterministic optimal control theory. The second part introduces stochastic optimal control for Markov diffusion processes. It also inlcudes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle. ... Read more

Book Description

A comprehensive introduction to convexity and optimization in Rn

This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material.

Convexity and Optimization in Rn provides detailed discussion of:

• Requisite topics in real analysis
• Convex sets
• Convex functions
• Optimization problems
• Convex programming and duality
• The simplex method

A detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes. ... Read more

Book Description

Computing has become essential for the modeling, analysis, and optimization of systems. This book is devoted to algorithms, computational analysis, and decision models. The chapters are organized in two parts: optimization models of decisions and models of pricing and equilibria.Optimization is at the core of rational decision making. Even when the decision maker has more than one goal or there is significant uncertainty in the system, optimization provides a rational framework for efficient decisions. The Markowitz mean-variance formulation is a classical example. The first part of the book is on recent developments in optimization decision models for finance and economics. The first four chapters of this part focus directly on multi-stage problems in finance. Chapters 5--8 involve the use of worst-case robust analysis. Chapters 9--11 are devoted to portfolio optimization. The final four chapters are on transportation-inventory with stochastic demand; optimal investment with CRRA utility; hedging financial contracts; and, automatic differentiation for computational finance.The uncertainty associated with prediction and modeling constantly requires the development of improved methods and models. Similarly, as systems strive towards equilibria, the characterization and computation of equilibria assists analysis and prediction. The second part of the book is devoted to recent research in computational tools and models of equilibria, prediction, and pricing. The first three chapters of this part consider hedging issues in finance. Chapters 19--22 consider prediction and modeling methodologies. Chapters 23--26 focus on auctions and equilibria. Volatility models are investigated in chapters 27--28. The final two chapters investigate risk assessment and product pricing.Audience: Researchers working in computational issues related to economics, finance, and management science. ... Read more

Book Description

Review of previous editions

‘Such a text — and this is the only one of this type I know of — should be the basis of all instruction in Mathematical Programming. Journal of the Royal Statistical Society

‘An excellent introduction … for students of business administration and people who want to see the utility of operations research. European Journal of Operational Research

‘It will be appreciated very much by practitioners who already have knowledge in the field of mathematical programming. Mathematical Programming Society Newsletter Model Building in Mathematical Programming Fourth Edition H. Paul Williams Faculty of Mathematical Studies, University of Southampton, UK

This extensively revised fourth edition of this well-known and much praised book contains a great deal of new material. In particular sections and new problems have been added covering Revenue Management. Hydro Electric Generation, Date Envelopment (efficiency) Analysis, Milk Distribution and Collection and Constraint Programming. The book discusses the general principles of model building in mathematical programming and shows how they can be applied by using simplified but practical problems from widely different contexts. Suggested formulations and solutions are given in the latter part of the book together with computational experience to give the reader a feel for the computation difficulty of solving that particular type of model. Aimed at undergraduates, postgraduates, research students and managers, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpretation of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. ... Read more

Reviews (4)

Excellent
If there is anything that I would hold against my favorite Operations Research books - it would be the lack of emphasis on model and structure. Williams' book fills in that gap and is an essential companion to every Math Prog book. It is not a cookbook where one can look up a particular problem and the possible ways to model it. Instead, it takes a systematic and very sensible approach to modeling.
The three chapters on Integer Programming Models are amazingly easy to understand and were a real help during a graduate course in the subject. The huge number of practical examples in Parts 2, 3 and 4 of the book is the real value of the book. I would be hard-pressed for space to describe the range of problems that are modeled in Part 2... Part 3 covers a good deal of discussion on these formulations and Part 4 follows it up with solutions. Though solutions are not discussed in detail, they are a great help for someone who has worked hard through the problems and needs a verification of the solutions.
Another useful section in the book is a chapter on the interpretation of Linear Programming solutions. For a person without a Math Prog background (say, a manager), this kind of material is very useful. In fact, it once served as a good refresher for me in a hurry... and an excellent one at that.
The only sore point is a very limited discussion on nonlinear models.

The Best Book of Its Kind
This is one of the only books I have ever encountered that focuses on the practical aspects of model formulation. This is a frequently overlooked aspect of optimization, but models that are well formulated will often result in superior performance. It is particularly strong in the formulation of mixed-integer problems, with a variety of tips for linearizing variable products and for incorporation of logical constructs. It also shows how to model SOS1 and SOS2 variable types. One other area that I found to be particularly useful was a section covering convexity analysis. This was the only book that I've read that did a good job of explaining the concepts and ramifications of problem convexity. Finally, the examples in the book cover a wide range of practical problems. Most are fairly simple, but do a good job of illustrating important techniques.

I highly recommend this book for linear and mixed-integer modelers. However, if you don't use these types of solvers in your work, the book is less likely to be valuable.

Good book for every one
Some books are good for mathematicians, some books are good for managers. This book is different. Williams did a good job to combine both mathematic and application perfective in a single book. Even you have only high school background, this book is readable. For senior researchers or grad students or strong math background person, this book is still enjoyable to recall your fundamental of math modeling. The references are not quite updated, however. Also, this book should added some current optimization tools. Even though the title is model building, not solving, it won't be harmful to have the metaheuristics (only introduction) or KKT.

It's so good!
The book is wonderful. If I have the money, I think I will buy it. Sigh! ... Read more

Book Description

This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. ... Read more

Reviews (1)

A good survey on approximation algorithms
Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. This book is actually a collection of survey articles written by some of the foremost experts in this field.

Many of these developments are due to Mathemtical programming (primal dual, semidefinite programming et al). The most exciting of these has been the Goemans and Williamson algorithm for MAX CUT and MAX SAT. A good account of these techniques appears in Chapters 4 and 11.

On the other hand a sequence of unexpected results in complexity culminated in a proof that many of these problems cannot have polynomial approximation algorithms unless P=NP. A good survey of "Hardness of Approximations" appears in Chapter 10, written by Sanjeev Arora and Carsten Lund both of whom were responsible for some original developments in this field.

I am going to purchase a copy of this book and can only strongly recommend it to everyone. ... Read more

Book Description

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. ... Read more

Book Description

This is an introduction to optimal control theory for systems governed by vector ordinary differential equations, up to and including a proof of the Pontryagin Maximum Principle. Though the subject is accessible to any student with a sound undergraduate mathematics background. Theory and applications are integrated with examples, particularly one special example (the rocket car) which relates all the abstract ideas to an understandable setting. The authors avoid excessive generalization, focusing rather on motivation and clear, fluid explanation. ... Read more

Book Description

This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented. ... Read more

Reviews (1)

A encyclopaedic reference on combinatorial optimization
A definitive account of the history and present state of combinatorial optimization from an author who is one of the most respected researchers in this area. The author has won the Dantzig award, the Fulkerson prize (twice) and the Lanchester Prize for his earlier classic text on "Theory of Linear and Integer Programming". Given the current pricing, it is a steal with over 1800 pages spread across three volumes. This is certainly not a text to be read from cover to cover but is a handy reference if you are interested in combinatorial optimization as a research topic or in the related areas of optimization, integer programming, polyhedral combinatorics, or graph theory.

The author gives short and elegants proof of most of the results. The reader is expected to have a background in graph theory, linear programming and integer programming. The author cites some results without proofs from his earlier books , "Theory of Linear and Integer Programming", and "Geometric Algorithms and Combinatorial Optimization". The book does not concentrate on applications and modeling aspects of combinatorial optimization problems and it does not dwell on the computational methods for NP-hard problems. The book does not offer exercises but lists some open problems and research topics (updated on author's website).

The book is mainly devoted to the theoretical developments in this field. Quoting the author, "We aim at offering an introduction and an in-depth survey of polyhedral combinatorics and efficient algorithms ... In the astonishing event that NP=P will be proved, this book will be highly incomplete". The results in this book are up to date till 2002 (updates are available at the author's website). In short this book should be invaluable for a graduate student or a researcher. ... Read more