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We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

Optimization and Control · Mathematics 2019-10-14 Nikitas Rontsis , Paul J. Goulart

In this work, we study a variant of nonnegative matrix factorization where we wish to find a symmetric factorization of a given input matrix into a sparse, Boolean matrix. Formally speaking, given $\mathbf{M}\in\mathbb{Z}^{m\times m}$, we…

Machine Learning · Computer Science 2022-01-14 Sitan Chen , Zhao Song , Runzhou Tao , Ruizhe Zhang

Let $G = (V,E,w)$ be a weighted undirected graph on $|V| = n$ vertices and $|E| = m$ edges, let $k \ge 1$ be any integer, and let $\epsilon < 1$ be any parameter. We present the following results on fast constructions of spanners with…

Data Structures and Algorithms · Computer Science 2021-08-03 Hung Le , Shay Solomon

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

Machine Learning · Computer Science 2010-11-17 Curzio Basso , Matteo Santoro , Alessandro Verri , Silvia Villa

Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…

Computational Complexity · Computer Science 2016-08-31 Massimo Cairo , Romeo Rizzi

Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…

Machine Learning · Computer Science 2023-07-18 Sebastian Dalleiger , Jilles Vreeken

We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…

Data Structures and Algorithms · Computer Science 2025-08-15 Huck Bennett , Karthik Gajulapalli , Alexander Golovnev , Evelyn Warton

Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…

Numerical Analysis · Mathematics 2014-05-16 John T. Holodnak , Ilse C. F. Ipsen

The problem of finding maximum (or minimum) witnesses of the Boolean product of two Boolean matrices (MW for short) has a number of important applications, in particular the all-pairs lowest common ancestor (LCA) problem in directed acyclic…

Data Structures and Algorithms · Computer Science 2021-06-01 Mirosław Kowaluk , Andrzej Lingas

The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…

Information Theory · Computer Science 2026-01-21 Hoang Ly , Emina Soljanin

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

Optimization and Control · Mathematics 2021-08-05 Reka A. Kovacs , Oktay Gunluk , Raphael A. Hauser

We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the…

Computer Science and Game Theory · Computer Science 2015-04-09 Fidaa Abed , Ioannis Caragiannis , Alexandros A. Voudouris

This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…

Optimization and Control · Mathematics 2021-08-13 Xuyang Wu , Jie Lu

We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…

Optimization and Control · Mathematics 2023-07-19 Salma Omer , Montaz Ali

In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…

Data Structures and Algorithms · Computer Science 2024-04-15 Ashish Gola , Igor Shinkar , Harsimran Singh

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…

Statistics Theory · Mathematics 2017-10-27 Yohann De Castro , Fabrice Gamboa , Didier Henrion , Roxana Hess , Jean-Bernard Lasserre

Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…

Data Structures and Algorithms · Computer Science 2012-09-21 Konstantin Kutzkov

Approximate computing is an emerging paradigm where design accuracy can be traded off for benefits in design metrics such as design area, power consumption or circuit complexity. In this work, we present a novel paradigm to synthesize…

Hardware Architecture · Computer Science 2018-05-17 Soheil Hashemi , Hokchhay Tann , Sherief Reda

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…

Computational Geometry · Computer Science 2022-07-15 Matthew J. Katz , Micha Sharir

Let 1_k 0_l denote the (k+l)\times 1 column of k 1's above l 0's. Let q. (1_k 0_l) $ denote the (k+l)xq matrix with q copies of the column 1_k0_l. A 2-design S_{\lambda}(2,3,v) can be defined as a vx(\lambda/3)\binom{v}{2} (0,1)-matrix with…

Combinatorics · Mathematics 2019-09-18 R. P. Anstee , Farzin Barekat