Approximation Algorithms

Book Description

This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms.

Richard Karp,University Professor, University of California at Berkeley

Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer.

It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic. I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms.

László Lovász, Senior Researcher, Microsoft Research

Customer Reviews:

a wide variety of topics.......2006-11-07

Vazirani's book seems well suited for a computer science researcher who has had a rigorous background in pure maths. The level of difficulty can be quite advanced. Also, it is not the sort of book that gives algorithm examples in an actual programming language. Not that this should be a handicap to a skilled reader. The algorithms are usually described in high level pseudocode. You have to manually instantiate these in the language of your preference.

The 30 chapters span a wide variety of computational topics. Some are simpler than others to understand. Like the chapter on finding the shortest vector from the integer lattice made from a set of linearly independent vectors. That requires only a year or so of introductory linear algebra.

There are exercises for each chapter. Some exercises are formidable. Essentially like little research problems in their own right. Another plus for the book.

Very nice introduction.......2006-05-20

This is a quite nice book by an author who is well-known in the field. The book is not thematic, instead it presents certain problems in each chapter along with the main approximation algorithms and correctness proofs. Yet, each new concept is well introduced with the problems. For instance, the author presents LP-based techniques on the same problem (set cover) in the second part of the book. This makes it quite easy to compare and understand different techniques. The last part of the book is a little bit advanced compared to the first two parts which uses combinatorial or LP-based analysis of the algorithms. The presentation of the PCP theorem- arguably the deepest theorem of computer science- and its consequences are also in the last part.

A warning though: The book is quite terse at times, which enforces a dense reading. This may not be suitable for an undergradute study. My only complaint is that the PCP theorem might well be introduced with a little more intution.

Overall, I rate this book as excellent. If you are interested in algorithms, you should definitely buy it. Also, buy the "Complexity and Approximation" by Ausiello, Crescenzi and others. They provide a more comprehensive and thematic treatment. It also has an excellent bibliography and list of NP-hard problems. These two will make a great couple. The book edited by Hochbaum (Approximation Algorithms for NP-hard problems) on the other hand presents detailed information on the algorithms.

Short and Sweet.......2006-03-13

This is a fanastic topics book in approximation algorithms. The problems and proofs are challenging and concise, but written in a very accessible manner. It is a great reference book, and also a convenient place to grab a lecture from if you need something to fill our a course. I have found it extremely useful, and even fun to read. I highly reccomend it for any person interested in theoretical computer science.

Much needed desktop reference for anyone working with algorithms, networking protocols, optimization.......2006-03-09

I have been looking for books related to solving NP-complete and NP-hard problems approximately. There is another book by Hochbaum and I have that too. Unfortunately, that book is more of a research oriented book as it is written by several researchers. It's like reading several research papers within two hard covers. This means that one needs to have a sort of intermediate level of experience with approximation algorithms.

For a beginner, one would expect a book that starts from ground-up and that has been written as a textbook rather than as a set of research papers. The book by Dr. Vazirani, is the only book that is written by one author with a step-by-step evolution of concepts and ideas related to approximation algorithms.

Only for graduate level - very good.......2005-11-22

Very good, it is easy to read the book if you have a good level
of knowledge and the experience to think some details in the
proofs of the theorems.
I think it is a very good book for a graduate student.

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.

Combinatorial Optimization: Theory and Algorithms (Algorithms and Combinatorics)

Average customer rating:

Useful yet dense!

Combinatorial Optimization: Theory and Algorithms (Algorithms and Combinatorics)
Bernhard Korte , and Jens Vygen
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 3540256849

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. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.

From the reviews of the 2nd edition:

"This book on combinatorial optimization is a beautiful example of the ideal textbook."

Operations Resarch Letters 33 (2005), p.216-217

"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."

OR News 19 (2003), p.42

Customer Reviews:

Useful yet dense!.......2001-11-13

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 force you to flip pages for a fwe minutes, just to remember the notation again.

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.

Combinatorial Optimization: Networks and Matroids

Average customer rating:

A good overview of combinatorial optimisation

Combinatorial Optimization: Networks and Matroids
Eugene Lawler
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486414531

Book Description

Perceptively written text examines optimization problems that can be formulated in terms of networks and algebraic structures called matroids. Chapters cover shortest paths, network flows, bipartite matching, nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. A suitable text or reference for courses in combinatorial computing.

Customer Reviews:

A good overview of combinatorial optimisation.......2001-04-20

Combinatorial Optimisation : Networks and Matroids by Eugene Lawler examines shortest paths, network flows, bipartite matching, non bipartite matching. More importantly there is an excellent introduction to matroid theory including matroids and the greedy algorithm, matroid intersections and matroid parity problems, some of these Lawler's own results.

However there is not much on NP completeness, since this book was published in 1976. For a more to date version of events in combinatorial optimisation one might want to look at Papadimitriou and Steglitz's book on combinatorial optimisation (quite old too, considering this was published in 1982), Ahuja, Magnanti and Orlin's book on Network algorithms, Hochbaum's book on approximation algorithms and Cook, Cunnigham,Pulleyblank and Schrijver's book on combinatorial optimisation (listed in the order they were published).

Book Description

A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics.
The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

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Complexity book
A great sequel to Garey and Johnson
A great sequel to Garey and Johnson

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
G. Ausiello , P. Crescenzi , V. Kann , Marchetti-sp , Giorgio Gambosi , and Alberto M. Spaccamela
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540654313

Book Description

This book is an up-to-date documentation of the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The well-structured wealth of problems, algorithms, results, and techniques introduced systematically will make the book an indispensible source of reference for professionals. The smooth integration of numerous illustrations, examples, and exercises make this monograph an ideal textbook.

Customer Reviews:

Complexity book.......2007-08-24

The book is excellent for teaching approximation algorithms. The book was new, but I benefit of a reduced price (probably promotional).

A great sequel to Garey and Johnson.......2001-03-30

This book is a great sequel to Garey and Johnson. The appendix of this book gives a list of all NP optimisation problems together with their current approximability (or inapproximability results) in a Garey Johnson fashion.

Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. There have been a number of exciting developments like semidefinite programming , the Goemans Williamson algorithm for max cut et al.

On the other hand, from a theoretical computer science point of view, we now have a proof that many of these problems cannot have polynomial approximation algorithms unless P=NP.

This book provides an excellent introduction to both areas. A worthy supplement to Garey and Johnson, Papadimitriou's books on combinatorial optimisation and computational complexity, Hochbaum's book on approximation algorithms, Alon and Spencer's book on the probabilistic method and finally Motwani and Raghavan's book on randomised algorithms.

A great sequel to Garey and Johnson.......2001-03-30

On the other hand, from a theoretical computer science point of view, we now have a proof that many of these problems cannot have polynomial approximation algorithms unless P=NP.

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