The main idea is to use the 2-prover game given by the Unique Games Conjecture as an "outer verifier" and build new probabilistically checkable proof systems (PCPs) on top of it.Expand

A conjecture regarding the power of unique 2-prover games is made, which is called the Unique Games Conjecture, that is, the maximum acceptance probability of the verifier over all the prover strategies.Expand

A stronger result is shown, namely, based on the same conjecture, vertex cover on k-uniform hypergraphs is hard to approximate within any constant factor better than k.Expand

Though it is unable to prove the majority is stablest conjecture, some partial results are enough to imply that MAX-CUT is hard to (3/4 + 1/(2/spl pi/) + /spl epsi/)-approximate (/spl ap/ .909155), assuming only the unique games conjecture.Expand

This paper shows a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of $\alpha_{\text{\tiny{GW}}} + \epsilon$ for all $\ep silon > 0$, and indicates that the geometric nature of the Goemans-Williamson algorithm might be intrinsic to the MAX- CUT problem.Expand

This paper disproves the non-uniform version of Arora, Rao and Vazirani's Conjecture (2004), asserting that the integrality gap of the sparsest cut SDP, with the triangle inequality constraints, is bounded from above by a constant.Expand

The results lead to an improved space complexity lower bound of /spl Omega/(n/sup 1-2/k//log n) for approximating the k/sup th/ frequency moment with a constant number of passes over the input, and a technical improvement if only one pass over theinput is permitted.Expand

A stronger result is shown, namely, that, based on the same conjecture, vertex cover on k-uniform hypergraphs is hard to approximate within any constant factor better than k.Expand

A new multilayered probabilistically checkable proof (PCP) construction that extends the Raz verifier is presented, enabling it to be proved that Ek-Vertex-Cover is NP-hard to approximate within a factor of $(k-1-\epsilon)$ for arbitrary constants $\ep silon>0$ and $k\ge 3$.Expand

A long code test with one free bit, completeness 1-epsilon and soundness delta is presented, and the following two inapproximability results are proved.Expand