Synopses & Reviews
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
Review
From the reviews: "Approximation algorithms is an area where much progress has been made in the last 10 years. The book under review is a very good help for understanding these results. In each of the 27 chapters an important combinatorial optimization problem is presented and one or more approximation algorithms for it are clearly and concisely described and analyzed. In this way most of the most important results from the approximation algorithm literature are covered, often more easily comprehensible than the original articles." (Viggo Kann, Zentralblatt MATH, Vol. 1005, 2003) "The book under review concentrates on the ... design and analysis of efficient approximation algorithms with good performance guarantees. It is possibly the first textbook to provide an extensive and systematic coverage of this topic. ... The book starts briskly, using simple examples to illustrate some of the key concepts and draw the reader rapidly in. ... Copious exercises are included to test and deepen the reader's understanding. ... It deserves a place in every computer science and mathematical library." (Mark R. Jerrum, Mathematical Reviews, 2002 h) "The book of Vijay Vazirani is not the first one dedicated to approximation algorithms ... . However it is, I believe, among the very best from a didactical point of view: this is the text I would chose, would I have to give a course on approximation algorithms ... . I suspect that for many researchers it would be the first one to consult ... . It is a must acquisition for libraries of computer science/engineering departments ... ." (Francesco Maffioli, Mathematical Methods of Operations Research, Vol. 56 (2), 2002) "The book gives an overview on the theory of approximation algorithms. It presents the most important problems, the basic methods and ideas which are used in this area. ... The book can be used for a graduate course on approximation algorithms. ... The chapters also contain a section of exercises, which can help the students to understand the material in a deeper way. ... On the other hand the book can be used by the researchers of the field ... ." (Csanád Imreh, Acta Scientiarum Mathematicarum, Vol. 68, 2002)
Review
From the reviews:
"Approximation algorithms is an area where much progress has been made in the last 10 years. The book under review is a very good help for understanding these results. In each of the 27 chapters an important combinatorial optimization problem is presented and one or more approximation algorithms for it are clearly and concisely described and analyzed. In this way most of the most important results from the approximation algorithm literature are covered, often more easily comprehensible than the original articles." (Viggo Kann, Zentralblatt MATH, Vol. 1005, 2003)
"The book under review concentrates on the ... design and analysis of efficient approximation algorithms with good performance guarantees. It is possibly the first textbook to provide an extensive and systematic coverage of this topic. ... The book starts briskly, using simple examples to illustrate some of the key concepts and draw the reader rapidly in. ... Copious exercises are included to test and deepen the reader's understanding. ... It deserves a place in every computer science and mathematical library." (Mark R. Jerrum, Mathematical Reviews, 2002 h)
"The book of Vijay Vazirani is not the first one dedicated to approximation algorithms ... . However it is, I believe, among the very best from a didactical point of view: this is the text I would chose, would I have to give a course on approximation algorithms ... . I suspect that for many researchers it would be the first one to consult ... . It is a must acquisition for libraries of computer science/engineering departments ... ." (Francesco Maffioli, Mathematical Methods of Operations Research, Vol. 56 (2), 2002)
"The book gives an overview on the theory of approximation algorithms. It presents the most important problems, the basic methods and ideas which are used in this area. ... The book can be used for a graduate course on approximation algorithms. ... The chapters also contain a section of exercises, which can help the students to understand the material in a deeper way. ... On the other hand the book can be used by the researchers of the field ... ." (Csanád Imreh, Acta Scientiarum Mathematicarum, Vol. 68, 2002)
Synopsis
Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell (1872-1970) Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed con jecture that P -=/= NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of ap proximation algorithms as it stands today. It is reasonable to expect the picture to change with time. This book is divided into three parts. In Part I we cover combinato rial algorithms for a number of important problems, using a wide variety of algorithm design techniques. The latter may give Part I a non-cohesive appearance. However, this is to be expected - nature is very rich, and we cannot expect a few tricks to help solve the diverse collection of NP-hard problems. Indeed, in this part, we have purposely refrained from tightly cat egorizing algorithmic techniques so as not to trivialize matters. Instead, we have attempted to capture, as accurately as possible, the individual character of each problem, and point out connections between problems and algorithms for solving them."
Synopsis
This monograph deals with designing polynomial time approximation algorithms for NP-hard combinatorial optimization problems. Although NP-complete problems do not offer footholds to find optimal solutions efficiently, they offer footholds to find near-optimal solutions efficiently. Designing polynomial time algorithms involves finding these footholds and exploiting them. The book discusses a wide range of combinatorial and LP-based algorithms in detail.
Synopsis
"Approximation algorithms are currently a central and fast-developing area of research in theoretical computer science. This monograph covers the basic techniques used in the latest research work, techniques that everyone in the field should know, and shows that they form the beginnings of a promising theory. The author consolidates progress made so far, including some very recent results, and makes a strong effort to convey the beauty and excitement of work in the field."
Synopsis
Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.
Description
Includes bibliographical references (p. [355]-370) and index.
Table of Contents
Introduction.-
I. Combinatorial Algorithms: Set cover. Steiner tree and TSP. Multiway cuts and
k-cuts.
k-center. Feedback vertex set. Shortest superstring. Knapsack. Bin packing. Minimum makespan scheduling. Euclidean TSP.-
II. LP-Based Algorithms: Introduction to LP-duality. Rounding applied to set cover. LP-duality based analysis for set cover. The primal-dual schema. Maximum satisfiability. Scheduling on unrelated parallel machines. Multicut and integer multicommodity flow in trees. Multiway cut. Multicut in general graphs. Sparsest cut. Steiner forest. Steiner network. Facility location.
k-median. Semidefinite programming.-
III. Other Topics: Counting problems. Shortest vector. Hardness of approximation. Open problems.