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.input I. A game G is described by sets X, Y, U, V, a predicate Q, a probability measure u (which makes use of a random string t), ... Question a is sent to prover P, and question y is sent to prover P2. 2. Prover P answers with an assignment for the variables zo., zh-, and zc., and prover P2 answers with an assignment for zy. 3.

Title | : | Lectures on Proof Verification and Approximation Algorithms |

Author | : | Ernst W. Mayr, Hans Jürgen Prömel, Angelika Steger |

Publisher | : | Springer - 2006-06-08 |

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