Related papers: On Metric Multi-Covering Problems
In this paper, we study the generalized problem that minimizes or maximizes a multi-order complex quadratic form with constant-modulus constraints on all elements of its optimization variable. Such a mathematical problem is commonly…
We address the problem of computing a Minimum Weighted Vertex Cover (MWVC) in a decentralized network. MWVC, a classical NP-hard problem, is foundational in applications such as network monitoring and resource placement. We propose a fully…
We study the problem of covering the maximum number of vertices in a graph by a collection of vertex-disjoint stars, each with a number of satellites in a given interval $[k, \ell]$, where $1 \le k < \ell$ and $\ell$ can be infinity. This…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…
We consider the multi-access coded caching problem, which contains a central server with $N$ files, $K$ caches with $M$ units of memory each and $K$ users where each one is connected to $L (\geq 1)$ consecutive caches, with a cyclic…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
We study the problem of multi-access coded caching (MACC): a central server has $N$ files, $K$ ($K \leq N$) caches each of which stores $M$ out of the $N$ files, $K$ users each of which demands one out of the $N$ files, and each user…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
In the Priority $k$-Supplier problem the input consists of a metric space $(F \cup C, d)$ over set of facilities $F$ and a set of clients $C$, an integer $k > 0$, and a non-negative radius $r_v$ for each client $v \in C$. The goal is to…
In the minimum Multicut problem, the input is an edge-weighted supply graph $G=(V,E)$ and a simple demand graph $H=(V,F)$. Either $G$ and $H$ are directed (DMulC) or both are undirected (UMulC). The goal is to remove a minimum weight set of…
We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…
In this paper, we study the weighted $k$-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) $k$-server problem which has a polynomial-time…
We provide a comprehensive study of a natural geometric optimization problem motivated by questions in the context of satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs (MSC), we are given a graph…
The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a…
In this paper, we present an efficient massively parallel approximation algorithm for the $k$-means problem. Specifically, we provide an MPC algorithm that computes a constant-factor approximation to an arbitrary $k$-means instance in…
One-way car-sharing systems are transportation systems that allow customers to rent cars at stations scattered around the city, use them for a short journey, and return them at any station. The maximum customers' satisfaction problem…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
In this article, we consider colorable variations of the Unit Disk Cover ({\it UDC}) problem as follows. {\it $k$-Colorable Discrete Unit Disk Cover ({\it $k$-CDUDC})}: Given a set $P$ of $n$ points, and a set $D$ of $m$ unit disks (of…
Consider the following problem: given a metric space, some of whose points are "clients", open a set of at most $k$ facilities to minimize the average distance from the clients to these facilities. This is just the well-studied $k$-median…