Lectures on Proof Verification and Approximation Algorithms [electronic resource] / edited by Ernst W. Mayr, Hans Jürgen Prömel, Angelika Steger.Material type: TextLanguage: English Series: Lecture Notes in Computer Science: 1367Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998Description: XII, 348 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540697015Subject(s): Computer science | Computer software | Electronic data processing | Computational complexity | Combinatorics | Mathematical optimization | Computer Science | Algorithm Analysis and Problem Complexity | Discrete Mathematics in Computer Science | Computation by Abstract Devices | Combinatorics | Calculus of Variations and Optimal Control; Optimization | Numeric ComputingAdditional physical formats: Printed edition:: No titleDDC classification: 005.1 LOC classification: QA76.9.A43Online resources: Click here to access online
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.
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.