Lectures on Proof Verification and Approximation Algorithms

• Corporate Author: SpringerLink (Online service)
• Other Authors: Mayr, Ernst W. (Editor, http://id.loc.gov/vocabulary/relators/edt), Prömel, Hans Jürgen (Editor, http://id.loc.gov/vocabulary/relators/edt), Steger, Angelika (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Edition: 1st ed. 1998.
• Series: Lecture Notes in Computer Science, 1367
• Subjects: Computers.; Algorithms.; Computer science-Mathematics.; Combinatorics.; Calculus of variations.; Theory of Computation.; Algorithm Analysis and Problem Complexity.; Discrete Mathematics in Computer Science.; Computation by Abstract Devices.; Calculus of Variations and Optimal Control; Optimization.

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-con...

Table of Contents:

• to the theory of complexity and approximation algorithms
• to randomized algorithms
• Derandomization
• Proof checking and non-approximability
• Proving the PCP-Theorem
• Parallel repetition of MIP(2,1) systems
• Bounds for approximating MaxLinEq3-2 and MaxEkSat
• Deriving non-approximability results by reductions
• Optimal non-approximability of MaxClique
• The hardness of approximating set cover
• Semidefinite programming and its applications to approximation algorithms
• Dense instances of hard optimization problems
• Polynomial time approximation schemes for geometric optimization problems in euclidean metric spaces.