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Electronic Colloquium on Computational Complexity

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All reports by Author Sanjeev Arora:

TR12-094 | 19th July 2012
Sanjeev Arora, Arnab Bhattacharyya, Rajsekar Manokaran, Sushant Sachdeva

Testing Permanent Oracles -- Revisited

Suppose we are given an oracle that claims to approximate the permanent for most matrices $X$, where $X$ is chosen from the Gaussian ensemble (the matrix entries are i.i.d. univariate complex Gaussians). Can we test that the oracle satisfies this claim? This paper gives a polynomial-time algorithm for the task.

... more >>>

TR10-066 | 14th April 2010
Sanjeev Arora, Rong Ge

Learning Parities with Structured Noise

Revisions: 1

In the {\em learning parities with noise} problem ---well-studied in learning theory and cryptography--- we
have access to an oracle that, each time we press a button,
returns a random vector $ a \in \GF(2)^n$ together with a bit $b \in \GF(2)$ that was computed as
$a\cdot u +\eta$, where ... more >>>

TR10-041 | 11th March 2010
Sanjeev Arora, Russell Impagliazzo, William Matthews, David Steurer

Improved Algorithms for Unique Games via Divide and Conquer

We present two new approximation algorithms for Unique Games. The first generalizes the results of Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi who give polynomial time approximation algorithms for graphs with high conductance. We give a polynomial time algorithm assuming only good local conductance, i.e. high conductance for small subgraphs. ... 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 >>>

TR04-117 | 1st December 2004
Michael Alekhnovich, Sanjeev Arora, Iannis Tourlakis

Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy

Lovasz and Schrijver described a generic method of tightening the LP and SDP relaxation for any 0-1 optimization problem. These tightened relaxations were the basis of several celebrated approximation algorithms (such as for MAX-CUT, MAX-3SAT, and SPARSEST CUT).

We prove strong nonapproximability results in this model for well-known problems such ... more >>>

TR98-008 | 15th January 1998
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy

Proof verification and the hardness of approximation problems.

We show that every language in NP has a probablistic verifier
that checks membership proofs for it using
logarithmic number of random bits and by examining a
<em> constant </em> number of bits in the proof.
If a string is in the language, then there exists a proof ... more >>>

TR97-003 | 29th January 1997
Sanjeev Arora, Madhu Sudan

Improved low-degree testing and its applications

NP = PCP(log n, 1) and related results crucially depend upon
the close connection between the probability with which a
function passes a ``low degree test'' and the distance of
this function to the nearest degree d polynomial. In this
paper we study a test ... more >>>

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