相关论文: Approximate Covering with Lower and Upper Bounds v…

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given…

In this paper, we study the hard uniform capacitated $k$- median problem using local search heuristic. Obtaining a constant factor approximation for the \ckm problem is open. All the existing solutions giving constant-factor approximation,…

We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…

We introduce the $(p,q)$-Fair Clustering problem. In this problem, we are given a set of points $P$ and a collection of different weight functions $W$. We would like to find a clustering which minimizes the $\ell_q$-norm of the vector over…

In a minimum $p$ union problem (Min$p$U), given a hypergraph $G=(V,E)$ and an integer $p$, the goal is to find a set of $p$ hyperedges $E'\subseteq E$ such that the number of vertices covered by $E'$ (that is $|\bigcup_{e\in E'}e|$) is…

In the metric multi-cover problem (MMC), we are given two point sets $Y$ (servers) and $X$ (clients) in an arbitrary metric space $(X \cup Y, d)$, a positive integer $k$ that represents the coverage demand of each client, and a constant…

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…

We consider the uncapacitated facility location problem with (linear) penalty function and show that a modified JMS algorithm, combined with a randomized LP rounding technique due to Byrka-Aardal[1], Li[14] and Li et al.[16] yields 1.488…

Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been widely studied, many real-world applications involve more nuanced…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

The approximate coherent state rank is the minimal number of (classical) coherent states required to approximate a continuous-variable bosonic quantum state and directly relates to the classical complexity of simulating bosonic…

In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…

We consider the problem of covering multiple submodular constraints. Given a finite ground set $N$, a cost function $c: N \rightarrow \mathbb{R}_+$, $r$ monotone submodular functions $f_1,f_2,\ldots,f_r$ over $N$ and requirements…

We study the problem of sensor placement in environments in which localization is a necessity, such as ad-hoc wireless sensor networks that allow the placement of a few anchors that know their location or sensor arrays that are tracking a…

We study the $k$-median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most $k$ facilities. The goal is to minimize the sum of distances from each client to its nearest open facility…

The composite L0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite L0 regularization (the L0 norm composed with a linear mapping) is usually bypassed through approximating the…

Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location…

This paper investigates the robust uncertain two-level cooperative set covering problem (RUTLCSCP). Given two types of facilities, which are called y-facility and z-facility. The problem is to decide which facilities of both types to be…

In this paper, we investigate geometrical properties of the rank metric space and covering properties of rank metric codes. We first establish an analytical expression for the intersection of two balls with rank radii, and then derive an…