The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization)

Book Description

The leading reference on probabilistic methods in combinatorics-now expanded and updated

When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30ew material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:
* Several improved as well as new results
* A continuous approach to discrete probabilistic problems
* Talagrand's Inequality and other novel concentration results
* A discussion of the connection between discrepancy and VC-dimension
* Several combinatorial applications of the entropy function and its properties
* A new section on the life and work of Paul Erdös-the developer of the probabilistic method

Download Description

The leading reference on probabilistic methods in combinatorics-now expanded and updated

When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:

Several improved as well as new results
A continuous approach to discrete probabilistic problems
Talagrand's Inequality and other novel concentration results
A discussion of the connection between discrepancy and VC-dimension
Several combinatorial applications of the entropy function and its properties
A new section on the life and work of Paul Erd��he developer of the probabilistic method

Customer Reviews:

Love, love, love this book..........2005-09-08

I happen to love studying probability theory and the probabilistic method and this is the book I come to time and time again. It is well organized and provides great, straightforward, insightful explanations. However, its main strength is its wealth of beautiful (fairly recently) results (in varied fields) which show the method coming to life. Can't recommend this enough...

Learn from the masters.......2001-07-04

This book shows you how to approach problems in discrete mathematics that don't seem to be probabilistic at all, and nonetheless to apply probabilistic methods to find extremely sharp results. The book is full of beautifully chosen examples worked out by the authors, who are world class researchers in this subject area. Should be on the bookshelf of everyone who uses discrete mathematics.

A very interesting book.......2000-09-14

I found this book very enjoyable to read. Although the underlying theme of the book is to demonstrate examples of proofs of existence of a property of a finite structure by showing the structure must have the property with positive probabiltiy, the book goes beyond this to cover areas such as circuit complexity and discrepancy theory that rely heavily on probabilistic arguments. A must read for anyone who wants to add probablistic tools to their toolbox for proving things about discrete structures.

A Java Library of Graph Algorithms and Optimization (Discrete Mathematics and Its Applications)

Average customer rating:

A very handy collection
Printout of Java programs
Useful problem-solving tool
A mere compendium of poorly written algorithms

A Java Library of Graph Algorithms and Optimization (Discrete Mathematics and Its Applications)
Hang T. Lau
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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An Inconvenient Truth

ASIN: 1584887184

Book Description

Because of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. Self-contained and largely independent, each topic starts with a problem description and an outline of the solution procedure, followed by its parameter list specification, source code, and a test example that illustrates the usage of the code. The book begins with a chapter on random graph generation that examines bipartite, regular, connected, Hamilton, and isomorphic graphs as well as spanning, labeled, and unlabeled rooted trees. It then discusses connectivity procedures, followed by a paths and cycles chapter that contains the Chinese postman and traveling salesman problems, Euler and Hamilton cycles, and shortest paths. The author proceeds to describe two test procedures involving planarity and graph isomorphism. Subsequent chapters deal with graph coloring, graph matching, network flow, and packing and covering, including the assignment, bottleneck assignment, quadratic assignment, multiple knapsack, set covering, and set partitioning problems. The final chapters explore linear, integer, and quadratic programming. The appendices provide references that offer further details of the algorithms and include the definitions of many graph theory terms used in the book.

Customer Reviews:

A very handy collection.......2007-04-15

There are many well-written textbooks that cover the theory
and algorithms on graphs and combinatorial optimization.
Very few provide the computer code for the methods. This
book offers an extensive collection of Java programs in
this area. Each program is self-contained and can be used
independently through parameter passing. The drawback of
the book is that the coding style is not object oriented,
and the programs would be difficult to maintain. The
description of the methods and their implementations is
terse. Hence the book is not intended as a learning text.
But the library of programs is a very convenient handy
device for students and researchers in locating solutions
to classroom didactic problems in graphs and optimization,
which apparently is the main objective of the book.

Printout of Java programs.......2007-03-27

This is my third review; my two previous reviews have been removed. I have already notified Amazon about this fact

As I have stated, book is just a printout of Java program, without any explanation how program is doing what is doing, what are program limitations in terms of memory, time and complexity. Programming style is mostly Fortran IV like. Programs are without single line of comment and with non-intuitive variable names, what makes modificatios difficult or impossible. Book can be useful for somebody who needs "black box" library, doesn't need to understand programs and trusts the author that programs fave no flaws

Useful problem-solving tool.......2007-02-09

This library of ready-to-use programs is extremely useful. I have used the programs with very minimal effort in obtaining solutions to some graph optimization problems. Unfortunately the programs are not well documented; it would be a challenge to make modifications to the code. However, the library serves as an ideal black box tool in solving most of the pedagogical graph theory and optimization problems, especially well suited for users who are not of much concern for the underlying methodology and implementation.

A mere compendium of poorly written algorithms.......2007-02-07

There are so many problems with this book, it's hard to know where to begin. So I don't come across as all and only negative, I will first give it credit for gathering together, at least in name a large number of graph processing algorithms.

That said, here are the problems:

The book is just a catalog of graph algorithms with poorly done documentation and even worse actual code. To wit:

*Each algorithm is preceded by a very brief explanation of what it does and some of the issues involved. Suffice it to say that it's the sparsest and most minimal explanation imaginable; if you don't already understand the issues involved, you probably won't after reading the short paragraph or two that precedes each algorithm / method.

*There is but ONE class and every bit of functionality is contained in its own individual, single static method. This "design" causes not a few of the methods to literally run to a thousand and more lines and contain dozens and dozens of (cryptically named) member variables.

So for instance, if you are interested in planarity testing, there's a "method" called planarityTesting that takes four parameters and returns true or false.

All well and good until you actually look at that method and see declared 51 , that's fifty-one, member variables. Each of these variables has poorly chosen names like, "wkpathfind2" and "store2" and "store3" and of course "store4" and "sortptr1" and "sortptr2". I thought this tactic of vowel-conserving naming of variables went out with the 8 + 3 DOS naming convention. At any rate, the cryptic naming scheme combined with the lack of javadoc combine to render each variable's purpose completely opaque. This makes it all but impossible to relate the code to the underlying graph theory.

Then comes the code.

Imagine a thousand and more lines, literally page after page after page of streaming code, all one single method, manipulating these cryptic variables in virtually uncommented ways.

That is pretty much what you get with this book. One algorithm after another after another.

I would say the following:
1) the author codes as if from another time. There is NO object-oriented design to this code whatsoever. None. Zero. Zip.

2)The methods are hundreds or thousands of lines of what amounts to undocumented symbol manipulation. There is small chance to learn anything from this book with respect to relating the code to graph theory.

3) I can say that, having implemented many of the algorithms in this book myself prior to buying this book, the book has contributed nothing to my understanding and further, that already understanding the issues surrounding many of these methods, that is being a qualified reader, is NOT sufficient to allow the reader to follow and understand the algorithms.

4) If you only want to use the (static) methods to return a value or ascertain some property of a graph and you don't care to understand how it works or why it works, then perhaps you'll be happy with this book, but then , why not release the object code as blackbox library? If the code was never meant to be read, and there is no attempt at explaining graph theory as it relates to the code, then what of value is left for the reader?

5) Finally, if the purpose of the book is deliver a good "black-box" library, readers should know that the actual implementation of the graph "object" chosen in this book makes will make that problematic. The book uses an adjacency matrix to represent the graph, a well known data structure in graph theory. Unfortunately, this data structure has the following well-known problem: it is only suitable for the rare instance of dense graphs. The runtime performance and memory demands of this data structure make it unsuitable to any but very very small graphs. Most graphs are neither very very small nor very very dense, (as dense is defined in graph theory), and for that reason almost all graph drawing packages opt for a linked-list data structure to represent the graph.

This is solidly the worst book on this subject I have yet encountered. Amazon offers a number of alternative books, including the fine Graph Algorithms, Third Edition by Robert Sedgewick and Michael Schidlowsky, a book I have no connection with whatsoever and two authors who are otherwise unknown to me. Bundle of Algorithms in Java, Third Edition (Parts 1-5): Fundamentals, Data Structures, Sorting, Searching, and Graph Algorithms, Third Edition

Combinatorial Optimization: Algorithms and Complexity

Average customer rating:

Excellent book!
Well written
Combinatorial Optimization: Algorithms and Complexity
A classic...
Mmm, algorithms....

Combinatorial Optimization: Algorithms and Complexity
Christos H. Papadimitriou , and Kenneth Steiglitz
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486402584

Book Description

Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. "Mathematicians wishing a self-contained introduction need look no further." — American Mathematical Monthly. 1982 edition.

Customer Reviews:

Excellent book!.......2007-06-05

This book is very good. However, it's dense, so you'll have to parse it carefully and never in a hurry.

Well written.......2007-04-06

I bought this book because I wanted to have theory on linear programming including duality, integer linear programming, typical graph algorithms and matroid theory in one book. Up to now I have read only most of the chapter on matroids and I would like to say a big thanks to the author.

Although you will not solve the world's problems with greedy algorithms, my mathematical part of the heart was pleased and satisfied by the theory which explained the very nice relation between matroids and greedy algorithms.

Maybe I will tell you more in a few months

Combinatorial Optimization: Algorithms and Complexity.......2007-02-18

The book's state is very good, so I am satisfied with it.

A classic..........2007-01-11

I won't lie to you: this book is well written but relatively hard to read. The subject is inherently difficult, after all! I highly suggest it, though, because the author is a recognized expert on the field and the price is relatively low. It's worth it even if you enjoy a few pages...

Mmm, algorithms...........2006-11-12

This is a very nice, self-contained introduction to linear programming, algorithm design and analysis, and computational complexity. The contents are as follows:

Chap. 1 Optimization Problems 1.1 Introduction; 1.2 Optimization Problems; 1.3 Neighborhoods; 1.4 Local and Global Optima; 1.5 Convex Sets and Functions; 1.6 Convex Programming Problems

Chap. 2 The Simplex Algorithm 2.1 Forms of the Linear Programming Problem; 2.2 Basic Feasible Solutions; 2.3 The Geometry of Linear Programs; 2.3.1 Linear and Affine Spaces; 2.3.2 Convex Polytopes; 2.3.3 Polytopes and LP; 2.4 Moving from bfs to bfs; 2.5 Organization of a Tableau; 2.6 Choosing a Profitable Column; 2.7 Degeneracy and Bland's Anticycling Algorithm; 2.8 Beginning the Simplex Algorithm; 2.9 Geometric Aspects of Pivoting

Chap. 3 Duality 3.1 The Dual of a Linear Program in General Form; 3.2 Complementary Slackness; 3.3 Farkas' Lemma; 3.4 The Shortest-Path Problem and Its Dual; 3.5 Dual Information in the Tableau; 3.6 The Dual Simplex Algorithm; 3.7 Interpretation of the Dual Simplex Algorithm

Chap. 4 Computational Considerations for the Simplex Algorithm 4.1 The Revised Simplex Algorithm; 4.2 Compuational Implications of the Revised Simplex Algorithm; 4.3 The Max-Flow Problem and Its Solution by the Revised Method; 4.4 Dantzig-Wolfe Decomposition

Chap. 5 The Primal-Dual Algorithm 5.1 Introduction; 5.2 The Primal-Dual Algorithm; 5.3 Comments on the Primal-Dual Algorithm; 5.4 The Primal-Dual Method Applied to the Shortest-Path Problem; 5.5 Comments on Methodology; 5.6 The Primal-Dual Method Applied to Max-Flow

Chap. 6 Primal-Dual Algorithms for Max-Flow and Shortest Path: Ford-Fulkerson and Dijkstra 6.1 The Max-Flow, Min-Cut Theorem; 6.2 The Ford and Fulkerson Labeling Algorithm; 6.3 The Question of Finiteness of the Labeling Algorithm; 6.4 Dijkstra's Algorithm; 6.5 The Floyd-Warshall Algorithm

Chap. 7 Primal-Dual Algorithms for Min-Cost Flow 7.1 The Min-Cost Flow Problem; 7.2 Combinatorializing the Capacities--Algorithm Cycle; 7.3 Combinatorializing the Cost--Algorithm Buildup; 7.4 An Explicit Primal-Dual Algorithm for the Hitchcock Problem--Algorithm Alphabeta; 7.5 A Transformation of Min-Cost Flow to Hitchcock; 7.6 Conclusion

Chap. 8 Algorithms and Complexity 8.1 Computability; 8.2 Time Bounds; 8.3 The Size of an Instance; 8.4 Analysis of Algorithms; 8.5 Polynomial-Time Algorithms; 8.6 Simplex Is Not a Polynomial-Time Algorithm; 8.7 The Ellipsoid Algorithm; 8.7.1 LP, LI, and LSI; 8.7.2 Affine Transformations and Ellipsoids; 8.7.3 The Algorithm; 8.7.4 Arithmetic Precision

Chap. 9 Efficient Algorithms for the Max-Flow Problem 9.1 Graph Search; 9.2 What Is Wrong With the Labeling Algorithm; 9.3 Network Labeling and Digraph Search; 9.4 An O(|V|²) Max-Flow Algorithm; 9.5 The Case of Unit Capacities

Chap. 10 Algorithms For Matching 10.1 The Matching Problem; 10.2 A Bipartite Matching Algorithm; 10.3 Bipartite Matching and Network Flow; 10.4 Nonbipartite Matching: Blossoms; 10.5 Nonbipartite Matching: An Algorithm

Chap. 11 Weighted Matching 11.1 Introduction; 11.2 The Hungarian Method for the Assignment Problem; 11.3 The Nonbipartite Weighted Matching Problem; 11.4 Conclusions

Chap. 12 Spanning Trees and Matroids 12.1 The Minimum Spanning Tree Problem; 12.2 An O(|E|log|V|) Algorithm for the Minimum Spanning Tree Problem; 12.3 The Greedy Algorithm; 12.4 Matroids; 12.5 The Intersection of Two Matroids; 12.6 On Certain Extensions of the Matroid Intersection Problem; 12.6.1 Weighted Matroid Intersection; 12.6.2 Matroid Parity; 12.6.3 The Intersection of Three Matroids

Chap. 13 Interger Linear Programming 13.1 Introduction; 13.2 Total Unimodularity; 13.3 Upper Bounds for Solutions of ILPs

Chap. 14 A Cutting-Plane Algorithm for Integer Linear Programs 14.1 Gomory Cuts; 14.2 Lexicography; 14.3 Finiteness of the Fractional Dual Algorithm; 14.4 Other Cutting-Plane Algorithms

Chap. 15 NP-Complete Problems 15.1 Introduction; 15.2 An Optimization Problem Is Three Problems; 15.3 The Classes P and NP; 15.4 Polynomial-Time Reductions; 15.5 Cook's Theorem; 15.6 Some Other NP-Complete Problems: Clique and the TSP; 15.7 More NP-Complete Problems: Matching, Covering, and Partitioning

Chap. 16 More About NP-Completeness 16.1 The Class co-NP; 16.2 Pseudo-Polynomial Algorithms and "Strong" NP-Complete Problems; 16.3 Special Cases and Generalizations of NP-Complete Problems; 16.3.1 NP-Completeness By Restriction; 16.3.2 Easy Special Cases of NP-Complete Problems; 16.3.3 Hard Special Cases of NP-Complete Problems; 16.4 A Glossary of Related Concepts; 16.4.1 Polynomial-Time Reductions; 16.4.2 NP-Hard problems; 16.4.3 Nondeterministic Turing Machines; 16.4.4 Polynomial-Space Complete Problems; 16.5 Epilogue

Chap. 17 Approximation Algorithms 17.1 Heuristics for Node Cover: An Example; 17.2 Approximation Algorithm for the Traveling Salesman Problem; 17.3 Approximation Schemes; 17.4 Negative Results

Chap. 18 Branch-and-Bound and Dynamic Programming 18.1 Branch-and-Bound for Integer Linear Programming; 18.2 Branch-and-Bound in a General Context; 18.3 Dominance Relations; 18.4 Branch-and-Bound Strategies; 18.5 Application to a Flowshop Scheduling Problem; 18.6 Dynamic Programming

Chap. 19 Local Search 19.1 Introduction; 19.2 Problem 1: The TSP; 19.3 Problem 2: Minimum-Cost Survivable Networks; 19.4 Problem 3: Topology of Offshore Natural Gas Pipeline Systems; 19.5 Problem 4: Uniform Graph Partitioning; 19.6 General Issues in Local Search; 19.7 The Geometry of Local Search; 19.8 An Example of a Large Minimal Exact Neighborhood; 19.9 The Complexity of Exact Local Search for the TSP

All chapters have problem sets and notes and references.

As can be seen, this book has a mighty amount of information, and it is amazingly well-explained. Of course, you need a firm grasp of your linear algebra, and some knowledge of very elementary calc./real analysis and graph theory (although most of the graph theory needed, technically speaking, is supplied in an appendix). You don't even really need to know a programming language, since the authors use a "pidgin algol," explained in yet another appendix, for most of the algorithm stuff; all it takes is an orderly thought process to follow it.

Despite the book's age, it mostly holds up very well in terms of topics and presentation. In the preface to the Dover edition, the authors briefly discuss some more current topics not dealt with in the text and make some (probably also out of date!) referrals for those wishing to "catch up." All in all, this book is a great value both as a text and a reference.

Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)

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Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
Dieter Jungnickel
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 3540219056

Book Description

From the reviews of the first edition:

".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..."

Mathematical Reviews 2002

This thoroughly revised new edition offers a new chapter on the network simplex algorithm and a section on the five color theorem. Moreover, numerous smaller changes and corrections have been made and several recent developments have been discussed and referenced.

Average customer rating:

Excellent book
One of the best...
great book
Learning, understanding, optimizing NP problem
An Encyclopedic reference for Integer Programming

Integer and Combinatorial Optimization
Laurence A. Wolsey , and George L. Nemhauser
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 0471359432

Book Description

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION

"This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima

"A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews

"[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews

"This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society

"This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London

Also of interest . . .

INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.

Customer Reviews:

Excellent book.......2007-09-19

An excellent book for combinatorial optimization. This book provides with the basis of the integer programming problems and theories behind it.

One of the best..........2002-07-19

I first used this book as a text for a graduate course in Integer Programming. At first it seemed to be a very poorly organized book, but as I read it and grew familiar with the subject, I realized that this is a hybrid textbook-handbook. Though the title says "Integer and Combinatorial", the authors go a step ahead and present topics in advanced linear programming, computational complexity, polyhedral theory in a fashion appropriate to the learning of this subject. The exercises are challenging and it has a very good list of references (only up to 1988). Our professor had to supplement the text with recent papers to cover the latest advances. My only complaint is that model formulation could have been dealt with in more detail. You might want to use HP Williams' "Model Building in Mathematical Programming" to look up good Math Prog models.
Though this is an excellent book in all respects, I would recommend Papadimitriou's older book on combinatorial optimization for a good discussion of P, NP problems and decision / optimization problems.

great book.......2001-12-30

Nemhauser is a great professor and this book is text book for IP. But this book requires that you are familiar with Linear programming. So read this book only after you had LP. Bertsimas book is really good for Lp. Or even Bazaara's book is a goo start.

This book starts with the mathematical basics behind linear programming and develops on these introducing new techniques like Bender's decomposition, various cuts, etc. The way the mathematics is dealt is flawless but I thought the methods required more examples for better understanding. But ofcourse the book had to be concise....

I have no opinion on the combinatorial optimisation part.

Learning, understanding, optimizing NP problem.......2000-12-27

Don't let the title fools you. This book goes beyond Integer and Combintarial optimization. While there are many books talk about NP and proof, this book makes you "understand" it! Still, I agree with others that this book is a reference tool for Integer and Combinatorial optimization. I'm so glad this book published in paperback so it will be more affordable for others.... still expensive though :(

An Encyclopedic reference for Integer Programming.......1999-04-18

A great book, with whatever information you need regarding integer programming and Combinatorial Optimisation. A bit out of date perhaps!

Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)

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Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Accessories:

ASIN: 3540249796

Book Description

‘Network’ is a heavily overloaded term, so that ‘network analysis’ means different things to different people. Specific forms of network analysis are used in the study of diverse structures such as the Internet, interlocking directorates, transportation systems, epidemic spreading, metabolic pathways, the Web graph, electrical circuits, project plans, and so on. There is, however, a broad methodological foundation which is quickly becoming a prerequisite for researchers and practitioners working with network models.

From a computer science perspective, network analysis is applied graph theory. Unlike standard graph theory books, the content of this book is organized according to methods for specific levels of analysis (element, group, network) rather than abstract concepts like paths, matchings, or spanning subgraphs. Its topics therefore range from vertex centrality to graph clustering and the evolution of scale-free networks.

In 15 coherent chapters, this monograph-like tutorial book introduces and surveys the concepts and methods that drive network analysis, and is thus the first book to do so from a methodological perspective independent of specific application areas.

Local Search in Combinatorial Optimization

Average customer rating:

Not Good as a Textbook or Study Reference

Local Search in Combinatorial Optimization

Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0691115222

Book Description

In the past three decades, local search has grown from a simple heuristic idea into a mature field of research in combinatorial optimization that is attracting ever-increasing attention. Local search is still the method of choice for NP-hard problems as it provides a robust approach for obtaining high-quality solutions to problems of a realistic size in reasonable time. Local Search in Combinatorial Optimization covers local search and its variants from both a theoretical and practical point of view, each topic discussed by a leading authority. This book is an important reference and invaluable source of inspiration for students and researchers in discrete mathematics, computer science, operations research, industrial engineering, and management science.

In addition to the editors, the contributors are Mihalis Yannakakis, Craig A. Tovey, Jan H. M. Korst, Peter J. M. van Laarhoven, Alain Hertz, Eric Taillard, Dominique de Werra, Heinz Mühlenbein, Carsten Peterson, Bo Söderberg, David S. Johnson, Lyle A. McGeoch, Michel Gendreau, Gilbert Laporte, Jean-Yves Potvin, Gerard A. P. Kindervater, Martin W. P. Savelsbergh, Edward J. Anderson, Celia A. Glass, Chris N. Potts, C. L. Liu, Peichen Pan, Iiro Honkala, and Patric R. J. Östergård.

Customer Reviews:

Not Good as a Textbook or Study Reference.......2007-02-20

I bought this book for a graduate course. Despite the applause I see in the back cover, it is not so good as a textbook. It might be good if you are well-versed in the lexicon of optimization and optimization is your main area, then I think this book is good to understand the quantitative as well as the qualitative dimensions of each technique. For a novice researcher or student in the field, this is not the right book.

Average customer rating:

Combinatorial Theory, 2nd Edition
Marshall Hall
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 0471315184

Book Description

Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.

Combinatorics (Wiley-Interscience Series in Discrete Mathematics and Optimization)

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The best combinatorics text I have seen so far
Author Responds
Who is the audience?

Combinatorics (Wiley-Interscience Series in Discrete Mathematics and Optimization)
Russell Merris
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 047126296X

Book Description

mathematical gem--freshly cleaned and polished
This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:
* Lively and engaging writing style
* Timely and appropriate examples
* Numerous well-chosen exercises
* Flexible modular format
* Optional sections and appendices
Highlights of Second Edition enhancements:
* Smoothed and polished exposition, with a sharpened focus on key ideas
* Expanded discussion of linear codes
* New optional section on algorithms
* Greatly expanded hints and answers section
* Many new exercises and examples

Customer Reviews:

The best combinatorics text I have seen so far.......2005-03-01

There is no question that combinatorics is becoming more important in the practice of computer science. While some of the most important techniques are covered in discrete mathematics courses, there is not enough breadth or depth in the coverage. As a consequence, one of my goals this upcoming year is to convince my colleagues at Mount Mercy to add a course in combinatorics to the curriculum. As part of the proposal, I need to create a list of resources and a sample schedule of topics to be covered. To begin this process, I studied several combinatorics texts and decided that this one was the best.
There are six chapters, and the titles are:

 Chapter 1 The mathematics of choice
 Chapter 2 The combinatorics of finite functions
 Chapter 3 Polya's theory of enumeration
 Chapter 4 Generating functions
 Chapter 5 Enumeration in graphs
 Chapter 6 Codes and designs

The coverage is thorough and the sequence has been structured to make the last four chapters independent. This necessitated the duplication of some definitions and theorems, but it is a sensible strategy. There is more than enough material for a one-semester course, so this increases the options available to an instructor. I often skip chapters in a textbook in order to cover a topic I consider critical and find it very helpful when the author repeats key definitions and theorems.
The style is mathematically rigorous, the approach is that of a mathematics textbook with the sequence being: theorem, proof, example(s). A large number of exercises are given at the end of each section and solutions/hints to the odd numbered ones are included. It is a sound combinatorics text and the one that I would most likely use if I ever teach such a course.

Published in Journal of Recreational Mathematics, reprinted with permission.

Author Responds.......2004-11-08

It is unfortunate that Amazon.com has attached to the second edition of this book a review of the first edition.

Who is the audience?.......2003-12-30

I used this book as a text for a junior-level course. The first two chapters are well-written, with useful exercises, and appropriate for the audience; later chapters are far more difficult, with uneven coverage, and the exercises are far less useful (I had to use other books for exercises, hand out extensive notes, etc.) These later chapters might be good for professional review, but not for students.
This is not just my perception; several students commented that the early part of the book was much better than the later part.

Combinatorial Engineering of Decomposable Systems (Combinatorial Optimization)

Average customer rating:

Combinatorial Engineering of Decomposable Systems (Combinatorial Optimization)
M.S. Levin
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0792349504

Book Description

Combinatorial Engineering of Decomposable Systems presents a morphological approach to the combinatorial design/synthesis of decomposable systems. Applications involve the following: design (e.g., information systems; user's interfaces; educational courses); planning (e.g., problem-solving strategies; product life cycles; investment); metaheuristics for combinatorial optimization; information retrieval; etc.

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