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Electronic Colloquium on Computational Complexity

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All reports by Author Prasad Raghavendra:

TR17-125 | 7th August 2017
Badih Ghazi, Pritish Kamath, Prasad Raghavendra

Dimension Reduction for Polynomials over Gaussian Space and Applications

In this work we introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure. As applications, we address the following problems:

(I) Computability of the Approximately Optimal Noise Stable function over Gaussian space:

The goal ... more >>>

TR15-082 | 13th May 2015
Boaz Barak, Ankur Moitra, Ryan O'Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, John Wright

Beating the random assignment on constraint satisfaction problems of bounded degree

We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where $D$ is a bound on the number of constraints that each variable occurs in. ... more >>>

TR15-007 | 8th January 2015
Jonah Brown-Cohen, Prasad Raghavendra

Combinatorial Optimization Algorithms via Polymorphisms

An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP $\Lambda$ is tractable if and only if there exist certain non-trivial operations known as polymorphisms to combine solutions to ... more >>>

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