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All reports by Author Muli Safra:

TR18-078 | 23rd April 2018
Subhash Khot, Dor Minzer, Dana Moshkovitz, Muli Safra

Small Set Expansion in The Johnson Graph

This paper studies expansion properties of the (generalized) Johnson Graph. For natural numbers
t < l < k, the nodes of the graph are sets of size l in a universe of size k. Two sets are connected if
their intersection is of size t. The Johnson graph arises often ... more >>>

TR18-006 | 10th January 2018
Subhash Khot, Dor Minzer, Muli Safra

Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion

Revisions: 2

We prove that pseudorandom sets in Grassmann graph have near-perfect expansion as hypothesized in [DKKMS-2]. This completes
the proof of the $2$-to-$2$ Games Conjecture (albeit with imperfect completeness) as proposed in [KMS, DKKMS-1], along with a
contribution from [BKT].

The Grassmann graph $Gr_{global}$ contains induced subgraphs $Gr_{local}$ that are themselves ... more >>>

TR17-094 | 25th May 2017
Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

On Non-Optimally Expanding Sets in Grassmann Graphs

The paper investigates expansion properties of the Grassmann graph,
motivated by recent results of [KMS, DKKMS] concerning hardness
of the Vertex-Cover and of the $2$-to-$1$ Games problems. Proving the
hypotheses put forward by these papers seems to first require a better
understanding of these expansion properties.

We consider the edge ... more >>>

TR16-198 | 14th December 2016
Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

Towards a Proof of the 2-to-1 Games Conjecture?

We propose a combinatorial hypothesis regarding a subspace vs. subspace agreement test, and prove that if correct it leads to a proof of the 2-to-1 Games Conjecture, albeit with imperfect completeness.

more >>>

TR15-011 | 22nd January 2015
Subhash Khot, Dor Minzer, Muli Safra

On Monotonicity Testing and Boolean Isoperimetric type Theorems

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we
give a monotonicity testing algorithm that makes $\tilde{O}(\sqrt{n}/\epsilon^2)$ non-adaptive queries to a function
$f:\{0,1\}^n \mapsto \{0,1\}$, always accepts a monotone function and rejects a function that is $\epsilon$-far from
being monotone ... more >>>

TR12-109 | 31st August 2012
Subhash Khot, Muli Safra, Madhur Tulsiani

Towards An Optimal Query Efficient PCP?

We construct a PCP based on the hyper-graph linearity test with 3 free queries. It has near-perfect completeness and soundness strictly less than 1/8. Such a PCP was known before only assuming the Unique Games Conjecture, albeit with soundness arbitrarily close to 1/16.

At a technical level, our ... more >>>

TR07-102 | 4th October 2007
Andrej Bogdanov, Muli Safra

Hardness amplification for errorless heuristics

An errorless heuristic is an algorithm that on all inputs returns either the correct answer or the special symbol "I don't know." A central question in average-case complexity is whether every distributional decision problem in NP has an errorless heuristic scheme: This is an algorithm that, for every &delta; > ... more >>>

TR05-058 | 24th May 2005
Sanjeev Arora, Eli Berger, Elad Hazan, Guy Kindler, Muli Safra

On Non-Approximability for Quadratic Programs

This paper studies the computational complexity of the following type of
quadratic programs: given an arbitrary matrix whose diagonal elements are zero, find $x \in \{-1,+1\}^n$ that maximizes $x^TA x$. This problem recently attracted attention due to its application in various clustering settings (Charikar and Wirth, 2004) as well as ... more >>>

TR96-047 | 2nd September 1996
Oded Goldreich, Muli Safra

A Combinatorial Consistency Lemma with application to the PCP Theorem

Revisions: 1

The current proof of the PCP Theorem (i.e., NP=PCP(log,O(1)))
is very complicated.
One source of difficulty is the technically involved
analysis of low-degree tests.
Here, we refer to the difficulty of obtaining strong results
regarding low-degree tests; namely, results of the type obtained and
used by ... more >>>

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