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Electronic Colloquium on Computational Complexity

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All reports by Author David Steurer:

TR13-179 | 15th December 2013
Irit Dinur, David Steurer

Direct Product Testing

A direct product is a function of the form $g(x_1,\ldots,x_k)=(g_1(x_1),\ldots,g_k(x_k))$. We show that the direct product property is locally testable with $2$ queries, that is, a canonical two-query test distinguishes between direct products and functions that are from direct products with constant probability.

This local testing question comes up ... more >>>

TR11-142 | 2nd November 2011
Boaz Barak, Parikshit Gopalan, Johan Hastad, Raghu Meka, Prasad Raghavendra, David Steurer

Making the long code shorter, with applications to the Unique Games Conjecture

Revisions: 1

The long code is a central tool in hardness of approximation, especially in
questions related to the unique games conjecture. We construct a new code that
is exponentially more ecient, but can still be used in many of these applications.
Using the new code we obtain exponential improvements over several ... more >>>

TR11-065 | 25th April 2011
Boaz Barak, Prasad Raghavendra, David Steurer

Rounding Semidefinite Programming Hierarchies via Global Correlation

We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method by providing a new SDP-hierarchy based algorithm for constraint satisfaction problems with ... more >>>

TR10-172 | 11th November 2010
Prasad Raghavendra, David Steurer, Madhur Tulsiani

Reductions Between Expansion Problems

The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. This hardness assumption is closely connected to the Unique Games Conjecture (Khot, STOC 2002). In particular, the Small-Set Expansion Hypothesis implies the Unique ... 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 >>>

TR09-129 | 30th November 2009
Boaz Barak, Moritz Hardt, Thomas Holenstein, David Steurer

Subsampling Semidefinite Programs and Max-Cut on the Sphere

Revisions: 1

We study the question of whether the value of mathematical programs such as
linear and semidefinite programming hierarchies on a graph $G$, is preserved
when taking a small random subgraph $G'$ of $G$. We show that the value of the
Goemans-Williamson (1995) semidefinite program (SDP) for \maxcut of $G'$ is
more >>>

TR09-125 | 24th November 2009
David Steurer, Nisheeth Vishnoi

Connections Between Unique Games and Multicut

In this paper we demonstrate a close connection between UniqueGames and
In MultiCut, one is given a ``network graph'' and a ``demand
graph'' on the same vertex set and the goal is to remove as few
edges from the network graph as ... more >>>

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