We prove that for any positive integer k, there is a constant ck such that a randomly selected set of cknk log n Boolean vectors with high probability supports a balanced k-wise i...
Linear programming decoding for low-density parity check codes (and related domains such as compressed sensing) has received increased attention over recent years because of its p...
Sanjeev Arora, Constantinos Daskalakis, David Steu...
We consider and analyze a new algorithm for balancing indivisible loads on a distributed network with n processors. The aim is minimizing the discrepancy between the maximum and m...
Algebraic codes that achieve list decoding capacity were recently constructed by a careful "folding" of the Reed-Solomon code. The "low-degree" nature of this f...
We design a linear time approximation scheme for the GaleBerlekamp Switching Game and generalize it to a wider class of dense fragile minimization problems including the Nearest C...
This paper studies constant-time approximation algorithms for problems on degree-bounded graphs. Let n and d be the number of vertices and the degree bound, respectively. This pap...
We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dime...
The "direct product code" of a function f gives its values on all k-tuples (f(x1), . . . , f(xk)). This basic construct underlies "hardness amplification" in c...
Russell Impagliazzo, Valentine Kabanets, Avi Wigde...
We consider matrix groups, specified by a list of generators, over finite fields. The two most basic questions about such groups are membership in and the order of the group. Even...