Lectures on Proof Verification and Approximation Algorithms

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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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.

• algorithm
• algorithms
• approximation algorithms
• complexity
• complexity theory
• optimization
• programming
• proof verification
• randomized computation
• verification
• algorithm analysis and problem complexity
• combinatorics

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