PCPs and Inapproximability: Expander Graphs and their Applications
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Course ”Proofs and Computers“, JASS’06 Probabilistically Checkable Proofs
Before introducing probabilistically checkable proofs, I shortly give an overview of the historical development in the field of inapproximability results which are closely related to PCPs. A foundational paper from Johnson in 1974 states approximation algorithms and inapproximability results for Max SAT, Set Cover, Independent Set, and Coloring. While the decision problems for various problems,...
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Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we will study random walks on general graphs, leading to a the randomized logspace algorit...
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In this lecture, we present a result of Khot, Kindler, Mossel and O’Donnell [1] which states that approximating MaxCut to within a factor αGW + ε, for any ε > 0, is “hard”. Here hardness is not based under the usual P 6= NP assumption, but rather a weaker conjecture called the Unique Games Conjecture (UGC). This conjecture was introduced by Khot [2] in 2002, and states that a certain very meani...
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تاریخ انتشار 2009