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Electronic Colloquium on Computational Complexity

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Reports tagged with Smooth Label cover:
TR10-177 | 16th November 2010
Venkatesan Guruswami, Prasad Raghavendra, Rishi Saket, Yi Wu

Bypassing UGC from some optimal geometric inapproximability results

Revisions: 1

The Unique Games conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in the Label Cover instance seems critical in these proofs. In this ... more >>>

TR11-119 | 4th September 2011
Subhash Khot, Preyas Popat, Nisheeth Vishnoi

$2^{\log^{1-\epsilon} n}$ Hardness for Closest Vector Problem with Preprocessing

We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\epsilon)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log ^{1-\epsilon}n}.$ This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta ... more >>>

TR12-145 | 31st October 2012
Cenny Wenner

Circumventing d-to-1 for Approximation Resistance of Satisfiable Predicates Strictly Containing Parity of Width at Least Four

HÃ¥stad established that any predicate $P \subseteq \{0,1\}^m$ containing parity of width at least three is approximation resistant for almost satisfiable instances. However, in comparison to for example the approximation hardness of Max-3SAT, the result only holds for almost satisfiable instances. This limitation was addressed by O'Donnell, Wu, and Huang ... more >>>

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