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The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…

Data Structures and Algorithms · Computer Science 2022-08-23 Yuki Amano

We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…

Data Structures and Algorithms · Computer Science 2016-10-10 Shi Li

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

Optimization and Control · Mathematics 2020-02-27 V. Peiris , N. Sharon , N. Sukhorukova J. Ugon

In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…

Data Structures and Algorithms · Computer Science 2015-05-05 Meirav Zehavi

The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing…

Machine Learning · Computer Science 2022-10-28 Shiqing Liu , Xueming Yan , Yaochu Jin

The multi allocation p-hub median problem (MApHM), the multi allocation uncapacitated hub location problem (MAuHLP) and the multi allocation p-hub location problem (MApHLP) are common hub location problems with several practical…

Discrete Mathematics · Computer Science 2023-07-17 Niklas Jost

Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…

Machine Learning · Statistics 2018-04-24 Hunter Lang , David Sontag , Aravindan Vijayaraghavan

Linear programming (LP) is an extremely useful tool and 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 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris , Shi Li , Thomas Pensyl , Aravind Srinivasan , Khoa Trinh

One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…

Discrete Mathematics · Computer Science 2015-03-17 José Verschae , Andreas Wiese

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…

Optimization and Control · Mathematics 2016-09-27 Chouzenoux Emilie , Pesquet Jean-Christophe

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Data Structures and Algorithms · Computer Science 2018-12-31 Maria-Florina Balcan , Colin White

Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…

Data Structures and Algorithms · Computer Science 2019-05-16 Siu-Wing Cheng , Yuchen Mao

Oblivious dimension reduction, \`{a} la the Johnson-Lindenstrauss (JL) Lemma, is a fundamental approach for processing high-dimensional data. We study this approach for Uniform Facility Location (UFL) on a Euclidean input…

Data Structures and Algorithms · Computer Science 2024-11-11 Lingxiao Huang , Shaofeng H. -C. Jiang , Robert Krauthgamer , Di Yue

We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…

Quantum Physics · Physics 2007-05-23 Stefan Heinrich

We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…

Mathematical Finance · Quantitative Finance 2026-04-07 Yunfei Peng , Pengyu Wei , Wei Wei

We study data clustering problems with $\ell_p$-norm objectives (e.g. $k$-Median and $k$-Means) in the context of individual fairness. The dataset consists of $n$ points, and we want to find $k$ centers such that (a) the objective is…

Data Structures and Algorithms · Computer Science 2021-06-24 Deeparnab Chakrabarty , Maryam Negahbani

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…

Data Structures and Algorithms · Computer Science 2018-04-09 Ravishankar Krishnaswamy , Shi Li , Sai Sandeep

In the Submodular Facility Location problem (SFL) we are given a collection of $n$ clients and $m$ facilities in a metric space. A feasible solution consists of an assignment of each client to some facility. For each client, one has to pay…

Data Structures and Algorithms · Computer Science 2022-11-11 Fateme Abbasi , Marek Adamczyk , Miguel Bosch-Calvo , Jarosław Byrka , Fabrizio Grandoni , Krzysztof Sornat , Antoine Tinguely