相关论文: Linear Programming Relaxations for Goldreich's Gen…

The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community…

Under the Strong Exponential Time Hypothesis, an integer linear program with $n$ Boolean-valued variables and $m$ equations cannot be solved in $c^n$ time for any constant $c < 2$. If the domain of the variables is relaxed to $[0,1]$, the…

In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…

We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…

Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…

Pseudorandomness has played a central role in modern cryptography, finding theoretical and practical applications to various fields of computer science. A function that generates pseudorandom strings from shorter but truly random seeds is…

In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…

The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some…

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…

Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…

A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…

We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form psi(P(x)), where P is a low-degree polynomial and psi is a function with small Lipschitz…

We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\prod_{i=1}^n…

Local pseudorandom generators are a class of fundamental cryptographic primitives having very broad applications in theoretical cryptography. Following Couteau et al.'s work in ASIACRYPT 2018, this paper further studies the concrete…

The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…

Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…

In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…

We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs). Denote $n$ and $w$ as the length and the width of a ROBP. We have the following results. For standard ROBPs, we give an…