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A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games). The value of a 2-prover game is the maximum acceptance probability of the verifier over all the prover strategies. We make the following conjecture regarding the power of unique(More)
Based on a conjecture regarding the power of unique 2-prover-1-round games presented in [Khot02], we show that vertex cover is hard to approximate within any constant factor better than 2. We actually show a stronger result, namely, based on the same conjecture, vertex cover on k-uniform hypergraphs is hard to approximate within any constant factor better(More)
In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into &ell;<sub>1</sub> with constant distortion. We show that for an arbitrarily small constant &#916; &gt; 0, for all large enough <i>n</i>, there is an <i>n</i>-point negative type metric which requires distortion at least (log log(More)
In this paper, we give evidence suggesting that MAX-CUT is NP-hard to approximate to within a factor of /spl alpha//sub cw/+ /spl epsi/, for all /spl epsi/ > 0, where /spl alpha//sub cw/ denotes the approximation ratio achieved by the Goemans-Williamson algorithm (1995). /spl alpha//sub cw/ /spl ap/ .878567. This result is conditional, relying on two(More)
  • Subhash Khot
  • 2004
Assuming that NP /spl nsube//spl cap//sub /spl epsi/> 0/ BPTIME(2/sup n/spl epsi//), we show that graph min-bisection, densest subgraph and bipartite clique have no PTAS. We give a reduction from the minimum distance of code problem (MDC). Starting with an instance of MDC, we build a quasi-random PCP that suffices to prove the desired inapproximability(More)
Given a <i>k</i>-uniform hyper-graph, the E<i>k</i>-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that E<i>k</i>-Vertex-Cover is NP-hard to approximate within factor <i>(k-1-&#949;)</i> for any <i>k(More)
We address well-studied problems concerning the learn-ability of parities and halfspaces in the presence of classification noise. Learning of parities under the uniform distribution with random classification noise, also called the noisy parity problem is a famous open problem in computational learning. We reduce a number of basic problems regarding(More)
Arora, Rao and Vazirani [2] showed that the standard semi-definite programming (SDP) relaxation of the Sparsest Cut problem with the <i>triangle inequality</i> constraints has an integrality gap of O(&#8730;log n). They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture (referred to as the(More)
Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2 − ε for minimizing the makespan in the assembly line problem. These results follow(More)
For arbitrarily small constants epsilon, delta &#x226B; 0$, we present a long code test with one free bit, completeness 1-epsilon and soundness delta. Using the test, we prove the following two inapproximability results:1. Assuming the Unique Games Conjecture of Khot, given an n-vertex graph that has two disjoint independent sets of size (1/2-epsilon)n(More)