Related papers: A scaling-invariant algorithm for linear programmi…
A recent work by [Larsen, SODA 2023] introduced a faster combinatorial alternative to Bansal's SDP algorithm for finding a coloring $x \in \{-1, 1\}^n$ that approximately minimizes the discrepancy $\mathrm{disc}(A, x) := | A x |_{\infty}$…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…
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…
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all $p$-tuples of orthonormal vectors in ${\mathbb R}^n$ satisfying $k$ additional linear…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
We assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different…
We study the bit complexity of inverting diagonally dominant matrices, which are associated with random walk quantities such as hitting times and escape probabilities. Such quantities can be exponentially small, even on undirected…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
In robot localisation and mapping, outliers are unavoidable when loop-closure measurements are taken into account. A single false-positive loop-closure can have a very negative impact on SLAM problems causing an inferior trajectory to be…
We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…
We study an important case of ILPs $\max\{c^Tx \ \vert\ \mathcal Ax = b, l \leq x \leq u,\, x \in \mathbb{Z}^{n t} \} $ with $n\cdot t$ variables and lower and upper bounds $\ell, u\in\mathbb Z^{nt}$. In $n$-fold ILPs non-zero entries only…
In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss principle of least constraint and solving it using dynamic programming. Our approach builds…
It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…
Solving (mixed) integer linear programs, (M)ILPs for short, is a fundamental optimization task. While hard in general, recent years have brought about vast progress for solving structurally restricted, (non-mixed) ILPs: $n$-fold, tree-fold,…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…