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On the power of unique 2-prover 1-round games
  • Subhash Khot
  • Mathematics, Computer Science
    STOC '02
  • 19 May 2002
TLDR
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.
On the power of unique 2-prover 1-round games
  • Subhash Khot
  • Computer Science
    Proceedings 17th IEEE Annual Conference on…
  • 2002
TLDR
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.
Vertex cover might be hard to approximate to within 2-epsilon
TLDR
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.
Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?
TLDR
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.
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
TLDR
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.
The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into l1
TLDR
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.
Near-optimal lower bounds on the multi-party communication complexity of set disjointness
TLDR
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.
Vertex cover might be hard to approximate to within 2-/spl epsiv/
  • Subhash Khot, O. Regev
  • Mathematics, Computer Science
    18th IEEE Annual Conference on Computational…
  • 7 July 2003
TLDR
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.
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
TLDR
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 $k\ge 3$.
Optimal Long Code Test with One Free Bit
  • N. Bansal, Subhash Khot
  • Mathematics, Computer Science
    50th Annual IEEE Symposium on Foundations of…
  • 25 October 2009
TLDR
A long code test with one free bit, completeness 1-epsilon and soundness delta is presented, and the following two inapproximability results are proved.
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