Related papers: An Approximation Algorithm for Optimal Subarchitec…

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

We consider two optimization problems in planar graphs. In Maximum Weight Independent Set of Objects we are given a graph $G$ and a family $\mathcal{D}$ of objects, each being a connected subgraph of $G$ with a prescribed weight, and the…

We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…

We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop…

We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…

This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…

We study the NP-complete Maximum Outerplanar Subgraph problem. The previous best known approximation ratio for this problem is 2/3. We propose a new approximation algorithm which improves the ratio to 7/10.

Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…

This work addresses two fundamental limitations in neural network approximation theory. We demonstrate that a three-dimensional network architecture enables a significantly more efficient representation of sawtooth functions, which serves…

We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…

We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…