Related papers: A Concentration Inequality for the Facility Locati…
In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the…
In traditional facility location problems, a set of points is provided, and the objective is to determine the best location for a new facility based on criteria such as minimizing cost, time, and distances between clients and facilities.…
We study local search algorithms for metric instances of facility location problems: the uncapacitated facility location problem (UFL), as well as uncapacitated versions of the $k$-median, $k$-center and $k$-means problems. All these…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we give a comprehensive convergence analysis on the FOCUSS…
This article presents a matheuristic algorithm for the single-source capacitated facility location problem (SSCFLP) and its variants: SSCFLP with K facilities (SSCKFLP), SSCFLP with contiguous service areas (CFLSAP), and SSCFLP with K…
We present the Condensate Theorem: attention sparsity is a learned topological property, not an architectural constraint. Through empirical analysis of trained language models, we find that attention mass concentrates on a distinct…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
This paper studies the problem of minimizing group-level inequity in facility location games on the real line, where agents belong to different groups and may act strategically. We explore a fairness-oriented objective that minimizes the…
Sparse Attention is a technique that approximates standard attention computation with sub-quadratic complexity. This is achieved by selectively ignoring smaller entries in the attention matrix during the softmax function computation.…
We consider a stochastic optimization problem involving two random variables: a context variable $X$ and a dependent variable $Y$. The objective is to minimize the expected value of a nonlinear loss functional applied to the conditional…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
We provide nearly optimal algorithms for online facility location (OFL) with predictions. In OFL, $n$ demand points arrive in order and the algorithm must irrevocably assign each demand point to an open facility upon its arrival. The…
The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum…
We consider the {\em mobile facility location} (\mfl) problem. We are given a set of facilities and clients located in a common metric space. The goal is to move each facility from its initial location to a destination and assign each…
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
When selecting locations for a set of facilities, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In…
The Metric $k$-median problem over a metric space $(\mathcal{X}, d)$ is defined as follows: given a set $L \subseteq \mathcal{X}$ of facility locations and a set $C \subseteq \mathcal{X}$ of clients, open a set $F \subseteq L$ of $k$…