Lectures on Proof Verification and Approximation Algorithms
Lectures on Proof Verification and Approximation Algorithms [electronic resource] /
edited by Ernst W. Mayr, Hans Jürgen Prömel, Angelika Steger.
- 1st ed. 1998.
- XII, 348 p. online resource.
- Lecture Notes in Computer Science, 1367 1611-3349 ; .
- Lecture Notes in Computer Science, 1367 .
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.
9783540697015
10.1007/BFb0053010 doi
Computer science.
Algorithms.
Computer science--Mathematics.
Discrete mathematics.
Mathematical optimization.
Calculus of variations.
Theory of Computation.
Algorithms.
Discrete Mathematics in Computer Science.
Discrete Mathematics.
Calculus of Variations and Optimization.
QA75.5-76.95
004.0151
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.
9783540697015
10.1007/BFb0053010 doi
Computer science.
Algorithms.
Computer science--Mathematics.
Discrete mathematics.
Mathematical optimization.
Calculus of variations.
Theory of Computation.
Algorithms.
Discrete Mathematics in Computer Science.
Discrete Mathematics.
Calculus of Variations and Optimization.
QA75.5-76.95
004.0151