相关论文: Column Bound for Orthogonal Matrix Factorization

The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…

For an arbitrary prime $p$ we prove that the proportion of entries divisible by $p$ in certain columns of the character table of the symmetric group $S_n$ tends to 1 as $n\to\infty$. This is done by finding lower bounds on the number of…

Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection,…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

We consider the following basic problem: given an $n$-variate degree-$d$ homogeneous polynomial $f$ with real coefficients, compute a unit vector $x \in \mathbb{R}^n$ that maximizes $|f(x)|$. Besides its fundamental nature, this problem…

We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…

We tackle the problem of accelerating column generation (CG) approaches to set cover formulations in operations research. At each iteration of CG we generate a dual solution that approximately solves the LP over all columns consisting of a…

The forbidden number forb$(m,F)$, which denotes the maximum number of distinct columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation of $F$, has been widely studied in extremal set theory. Recently,…

We consider the problem of multiplying sparse matrices (over a semiring) where the number of non-zero entries is larger than main memory. In the classical paper of Hong and Kung (STOC '81) it was shown that to compute a product of dense $U…

We show that for any regular matroid on $m$ elements and any $\alpha \geq 1$, the number of $\alpha$-minimum circuits, or circuits whose size is at most an $\alpha$-multiple of the minimum size of a circuit in the matroid is bounded by…

Orthogonal matching pursuit~(OMP) is a commonly used greedy algorithm for recovering sparse signals from compressed measurements. In this paper, we introduce a variant of the OMP algorithm to reduce the complexity of reconstructing a class…

In a column-restricted covering integer program (CCIP), all the non-zero entries of any column of the constraint matrix are equal. Such programs capture capacitated versions of covering problems. In this paper, we study the approximability…

Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an \emph{orthogonal representation} that describes the desired…

We provide an explicit construction and direct proof for the lower bound on the number of first order oracle accesses required for a randomized algorithm to minimize a convex Lipschitz function.

We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…

The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every straight line passing through S. In spite of its simplicity,…

This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and…

The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…

In the Metric Capacitated Covering (MCC) problem, given a set of balls $\mathcal{B}$ in a metric space $P$ with metric $d$ and a capacity parameter $U$, the goal is to find a minimum sized subset $\mathcal{B}'\subseteq \mathcal{B}$ and an…

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…