Lectures on Proof Verification and Approximation Algorithms

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 proofsand 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.

List 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.

Product details

• Assisted by: Han Jürgen Prömel (Editor), Hans Jürgen Prömel (Editor), Ernst Mayr (Editor), Ernst W. Mayr (Editor), Hans Jürgen Prömel (Editor), Hans-Jürgen Prömel (Editor), Angelika Steger (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.1960
• EAN: 9783540642015
• ISBN: 978-3-540-64201-5
• No. of pages: 348
• Weight: 488 g
• Illustrations: XII, 348 p.
• Series: Lecture Notes in Computer Science; Lecture Notes in Computer Science
• Subject: Natural sciences, medicine, IT, technology > IT, data processing > IT