Related papers: On the Computational Complexity of Linear Discrepa…
In breakthrough work, Tardos (Oper. Res. '86) gave a proximity based framework for solving linear programming (LP) in time depending only on the constraint matrix in the bit complexity model. In Tardos's framework, one reduces solving the…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
We study one of the key tools in data approximation and optimization: low-discrepancy colorings. Formally, given a finite set system $(X,\mathcal S)$, the \emph{discrepancy} of a two-coloring $\chi:X\to\{-1,1\}$ is defined as $\max_{S \in…
Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
An $\epsilon$-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most $\epsilon$ from each other. Given a set of points and a set of objects,…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…