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Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2022-09-26 Agniva Chowdhury , Gregory Dexter , Palma London , Haim Avron , Petros Drineas

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called $2$-stage stochastic. A $2$-stage stochastic ILP is an integer program of the form $\min…

Computational Complexity · Computer Science 2021-02-08 Klaus Jansen , Kim-Manuel Klein , Alexandra Lassota

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms.…

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

Machine Learning · Computer Science 2022-08-12 Jerome Taupin , Yassir Jedra , Alexandre Proutiere

In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…

Computational Complexity · Computer Science 2022-12-12 Lijie Chen , Shafi Goldwasser , Kaifeng Lyu , Guy N. Rothblum , Aviad Rubinstein

For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…

Optimization and Control · Mathematics 2025-05-07 Naghmeh Shahverdi , Seyyedmahsa Banihashemi , David Bremner

We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…

Information Theory · Computer Science 2022-11-16 Elyassaf Loyfer , Nati Linial

Integer linear programs (ILPs) are a widely applied framework for dealing with combinatorial problems that arise in practice. It is known, e.g., by the success of CPLEX, that preprocessing and simplification can greatly speed up the process…

Computational Complexity · Computer Science 2013-02-18 Stefan Kratsch

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,…

Computational Geometry · Computer Science 2020-05-19 Dror Aiger , Haim Kaplan , Micha Sharir

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…

Data Structures and Algorithms · Computer Science 2021-12-24 Oliver Gebhard , Max Hahn-Klimroth , Olaf Parczyk , Manuel Penschuck , Maurice Rolvien , Jonathan Scarlett , Nelvin Tan

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high…

Artificial Intelligence · Computer Science 2024-01-17 Taoan Huang , Aaron Ferber , Yuandong Tian , Bistra Dilkina , Benoit Steiner

We study the standard-form ILP problem $\max\{ c^\top x \colon A x = b,\; x \in Z_{\geq 0}^n \}$, where $A\in Z^{k\times n}$ has full row rank. We obtain refined FPT algorithms parameterized by $k$ and $\Delta$, the maximum absolute value…

Data Structures and Algorithms · Computer Science 2026-04-16 Dmitry Gribanov , Tagir Khayaleyev , Mikhail Cherniavskii , Maxim Klimenko , Dmitry Malyshev , Stanislav Moiseev

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…

Data Structures and Algorithms · Computer Science 2018-11-05 Klaus Jansen , Alexandra Lassota , Lars Rohwedder

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

Data Structures and Algorithms · Computer Science 2010-11-01 Yuichi Yoshida

We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant…

Data Structures and Algorithms · Computer Science 2019-08-02 Anna Karlin , Nathan Klein , Shayan Oveis Gharan

Factor-revealing linear programs (LPs) and policy-revealing LPs arise in various contexts of algorithm design and analysis. They are commonly used techniques for analyzing the performance of approximation and online algorithms, especially…

Data Structures and Algorithms · Computer Science 2025-03-20 Pan Xu

In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…

Data Structures and Algorithms · Computer Science 2026-03-27 Christian Schulz , Jakob Ternes , Henning Woydt

We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…

Optimization and Control · Mathematics 2025-02-20 Xavier Allamigeon , Daniel Dadush , Georg Loho , Bento Natura , László A. Végh

We describe a variation of the iterative closest point (ICP) algorithm for aligning two point sets under a set of transformations. Our algorithm is superior to previous algorithms because (1) in determining the optimal alignment, it…

Graphics · Computer Science 2009-09-29 Jeff M. Phillips , Ran Liu , Carlo Tomasi

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…

Statistics Theory · Mathematics 2011-06-14 Pierre Del Moral , Arnaud Doucet , Sumeetpal Singh