Related papers: On the hardness of learning sparse parities

Let n denote the number of variables and m the number of equations in a sparse polynomial system over the binary field. We study the inconsistency probability of randomly generated sparse polynomial systems over the binary field, where each…

We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…

One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…

We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…

We propose a quantum data fitting algorithm for non-sparse matrices, which is based on the Quantum Singular Value Estimation (QSVE) subroutine and a novel efficient method for recovering the signs of eigenvalues. Our algorithm generalizes…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k,…

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most $k$ nonzero elements, where $k$ is…

A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…

We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…

We demonstrate that the best $k$-sparse approximation of a length-$n$ vector can be recovered within a $(1+\epsilon)$-factor approximation in $O((k/\epsilon) \log n)$ time using a non-adaptive linear sketch with $O((k/\epsilon) \log n)$…

Consider the fundamental task of finding independent sets of (constant) size $k$ in a given $n$-node hypergraph. How is the time complexity affected by the sparsity of the input, i.e., the number of hyperedges $m$? Tur\'{a}n's theorem…

The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code…

Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…

The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…

This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…

In this work, we study the hardness of approximation of the fair $k$-center problem. In this problem, we are given a set of data points in a metric space that is partitioned into groups and the task is to choose a subset of $k$-data points,…

We investigate the question whether Subset Sum can be solved by a polynomial-time algorithm with access to a certificate of length poly(k) where k is the maximal number of bits in an input number. In other words, can it be solved using only…

We give an algebraic, determinant-based algorithm for the K-Cycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the $O^*(2^{|K|})$…

In view of the KS-tensor complementarity problem, the sparse solution of this problem is studied. Due to the nonconvexity and noncontinuity of the l_0-norm, it is a NP hard problem to find the sparse solution of the KS-tensor…

In the classical Subset Sum problem we are given a set $X$ and a target $t$, and the task is to decide whether there exists a subset of $X$ which sums to $t$. A recent line of research has resulted in $\tilde{O}(t)$-time algorithms, which…