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Lectures on Proof Verification and Approximation Algorithms

  • Textbook
  • © 1998

Overview

Editors:
  1. Ernst W. Mayr
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  2. Hans Jürgen Prömel
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  3. Angelika Steger
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  • This book coherently summarizes the spectacular progress achieved in the areas of approximation algorithms and combinatorial optimization during the last few years.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 1367)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-4
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  2. Introduction to the theory of complexity and approximation algorithms

    • Thomas Jansen
    Pages 5-28

  3. Introduction to randomized algorithms

    • Artur Andrzejak
    Pages 29-39

  4. Derandomization

    • Detlef Sieling
    Pages 41-61

  5. Proof checking and non-approximability

    • Stefan Hougardy
    Pages 63-82

  6. Proving the PCP-Theorem

    • Volker Heun, Wolfgang Merkle, Ulrich Weigand
    Pages 83-160

  7. Parallel repetition of MIP(2,1) systems

    • Clemens Gröpl, Martin Skutella
    Pages 161-177

  8. Bounds for approximating MaxLinEq3-2 and MaxEkSat

    • Sebastian Seibert, Thomas Wilke
    Pages 179-211

  9. Deriving non-approximability results by reductions

    • Claus Rick, Hein Röhrig
    Pages 213-233

  10. Optimal non-approximability of MaxClique

    • Mastin Mundhenk, Anna Slobodová
    Pages 235-248

  11. The hardness of approximating set cover

    • Alexander Wolff
    Pages 249-262

  12. Semidefinite programming and its applications to approximation algorithms

    • Thomas Hofmeister, Martin Hühne
    Pages 263-298

  13. Dense instances of hard optimization problems

    • Katja Wolf
    Pages 299-311

  14. Polynomial time approximation schemes for geometric optimization problems in euclidean metric spaces

    • Richard Mayr, Annette Schelten
    Pages 313-323

  15. Back Matter

    Pages 325-334
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Keywords

About this book

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.

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