PCP and Hardness of Approximation

The PCP Theorem and Hardness of Approximation

In this report, we give a brief overview of Probabilistically Chekable proofs, and present Irit Dinur’s proof of the celebrated PCP theorem. We also briefly deal with the importance of the PCP theorem in deciding hardness of approximation of various problems.

Cse 533: the Pcp Theorem and Hardness of Approximation Lecture 20: Course Summary and Open Problems

– PCP theorem. The classic PCP theorem is most useful for proving that optimization problems have no PTAS. – E3LIN2. The 1− 2 vs 1/2− 2 hardness of this problem is most useful for proving that problems have no approximation beyond a fixed constant factor; i.e., for statements like “such-and-such maximization problem has no 77 78 -approximation unless P = NP”. – Raz’s Label Cover. The hardness o...

The PCP theorem and hardness of approximation

An Introduction to the Pcp Theorem

In this paper, we will first define basic concepts in computational complexity. Then, we will introduce the PCP Theorem and its equivalent formulation from the hardness of approximation view. Finally, we will prove a weaker version of the PCP theorem.

Probabilistic Checking of Proofs and Hardness of Approximation

This paper introduces basic notions of classic computational complexity theory and probabilistically checkable proof. It sketches the proof of the PCP theorem, and discusses its applications to the hardness of approximation of various problems.

Nov 15 & 17 , 2011 ) : Hardness of Approximation , PCP theorem

So far we have been mostly talking about designing approximation algorithms and proving upper bounds. From no until the end of the course we will be talking about proving lower bounds (i.e. hardness of approximation). We are familiar with the theory of NP-completeness. When we prove that a problem is NP-hard it implies that, assuming P 6=NP there is no polynomail time algorithm that solves the ...