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Approximation Algorithms

  • Book
  • © 2003

Overview

Authors:
  1. Vijay V. Vazirani

    1. Georgia Institute of Technology, College of Computing, Atlanta, USA

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  • Spreads powerful algorithmic ideas developed in this area to practitioners
  • Will accelerate progress in this area
  • Raises algorithmic awareness of the scientific community by showing simple ways of expressing complex algorithmic ideas
  • An indispensable cookbook for all serious mathematical programmers
  • Includes supplementary material: sn.pub/extras

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Table of contents (30 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Introduction

    1. Introduction

      • Vijay V. Vazirani
      Pages 1-11

  3. Combinatorial Algorithms

    1. Front Matter

      Pages 13-13
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    2. Set Cover

      • Vijay V. Vazirani
      Pages 15-26

    3. Steiner Tree and TSP

      • Vijay V. Vazirani
      Pages 27-37

    4. Multiway Cut and k-Cut

      • Vijay V. Vazirani
      Pages 38-46

    5. k-Center

      • Vijay V. Vazirani
      Pages 47-53

    6. Feedback Vertex Set

      • Vijay V. Vazirani
      Pages 54-60

    7. Shortest Superstring

      • Vijay V. Vazirani
      Pages 61-67

    8. Knapsack

      • Vijay V. Vazirani
      Pages 68-73

    9. Bin Packing

      • Vijay V. Vazirani
      Pages 74-78

    10. Minimum Makespan Scheduling

      • Vijay V. Vazirani
      Pages 79-83

    11. Euclidean TSP

      • Vijay V. Vazirani
      Pages 84-89

  4. LP-Based Algorithms

    1. Front Matter

      Pages 91-91
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    2. Introduction to LP-Duality

      • Vijay V. Vazirani
      Pages 93-107

    3. Set Cover via Dual Fitting

      • Vijay V. Vazirani
      Pages 108-117

    4. Rounding Applied to Set Cover

      • Vijay V. Vazirani
      Pages 118-123

    5. Set Cover via the Primal-Dual Schema

      • Vijay V. Vazirani
      Pages 124-129

    6. Maximum Satisfiability

      • Vijay V. Vazirani
      Pages 130-138

    7. Scheduling on Unrelated Parallel Machines

      • Vijay V. Vazirani
      Pages 139-144
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Keywords

About this book

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.

Reviews

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 asection 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)

Authors and Affiliations

  • Georgia Institute of Technology, College of Computing, Atlanta, USA

    Vijay V. Vazirani

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