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Electronic Colloquium on Computational Complexity

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All reports by Author Shmuel Safra:

TR03-020 | 27th March 2003
Elad Hazan, Shmuel Safra, Oded Schwartz

On the Hardness of Approximating k-Dimensional Matching

We study bounded degree graph problems, mainly the problem of
k-Dimensional Matching \emph{(k-DM)}, namely, the problem of
finding a maximal matching in a k-partite k-uniform balanced
hyper-graph. We prove that k-DM cannot be efficiently approximated
to within a factor of $ O(\frac{k}{ \ln k}) $ unless $P = NP$.
This ... more >>>

TR01-104 | 17th December 2001
Irit Dinur, Shmuel Safra

The Importance of Being Biased

We show Minimum Vertex Cover NP-hard to approximate to within a factor
of 1.3606. This improves on the previously known factor of 7/6.

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TR01-036 | 2nd May 2001
Amnon Ta-Shma, David Zuckerman, Shmuel Safra

Extractors from Reed-Muller Codes

Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. This research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, was noticed before. Yet, ... more >>>

TR98-066 | 3rd November 1998
Irit Dinur, Eldar Fischer, Guy Kindler, Ran Raz, Shmuel Safra

PCP Characterizations of NP: Towards a Polynomially-Small Error-Probability

This paper strengthens the low-error PCP characterization of NP, coming
closer to the ultimate BGLR conjecture. Namely, we prove that witnesses for
membership in any NP language can be verified with a constant
number of accesses, and with an error probability exponentially
small in the ... more >>>

TR98-048 | 6th July 1998
Irit Dinur, Guy Kindler, Shmuel Safra

Approximating CVP to Within Almost Polynomial Factor is NP-Hard

This paper shows finding the closest vector in a lattice
to be NP-hard to approximate to within any factor up to
$2^{(\log{n})^{1-\epsilon}}$ where
$\epsilon = (\log\log{n})^{-\alpha}$
and $\alpha$ is any positive constant $<{1\over 2}$.

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