Related papers: Set It and Forget It: Approximating the Set Once S…
We investigate the problem of optimally assigning a large number of robots (or other types of autonomous agents) to guard the perimeters of closed 2D regions, where the perimeter of each region to be guarded may contain multiple disjoint…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
In the Set Cover problem, the input is a ground set of $n$ elements and a collection of $m$ sets, and the goal is to find the smallest sub-collection of sets whose union is the entire ground set. The fastest algorithm known runs in time…
In this paper, we study the set cover problem in the fully dynamic model. In this model, the set of active elements, i.e., those that must be covered at any given time, can change due to element arrivals and departures. The goal is to…
The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…
We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…
Given an $n$-vertex bipartite graph $I=(S,U,E)$, the goal of set cover problem is to find a minimum sized subset of $S$ such that every vertex in $U$ is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
This paper considers a single-hop wireless network where a central node (or fusion center, FC) collects data from a set of m energy harvesting (EH) nodes (e.g. nodes of a wireless sensor network). In each time slot, k of m nodes can be…
We consider a strategic network monitoring problem involving the operator of a networked system and an attacker. The operator aims to randomize the placement of multiple protected sensors to monitor and protect components that are…
Coverage problem in wireless sensor networks measures how well a region or parts of it is sensed by the deployed sensors. Definition of coverage metric depends on its applications for which sensors are deployed. In this paper, we introduce…
We carry out a structural and algorithmic study of a mobile sensor coverage optimization problem targeting 2D surfaces embedded in a 3D workspace. The investigated settings model multiple important applications including camera network…
Homology theory has attracted great attention because it can provide novel and powerful solutions to address coverage problems in wireless sensor networks. They usually use an easily computable algebraic object, Rips complex, to detect…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different…
We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against $N\geq 2$ intruders. Upon…
In (fully) dynamic set cover, the goal is to maintain an approximately optimal solution to a dynamically evolving instance of set cover, where in each step either an element is added to or removed from the instance. The two main desiderata…
Geometric set cover is a classical problem in computational geometry, which has been extensively studied in the past. In the dynamic version of the problem, points and ranges may be inserted and deleted, and our goal is to efficiently…
A wireless network's design must include the optimization of the area of coverage of its wireless transmitters - mobile and base stations in cellular networks, wireless access points in WLANs, or nodes on a transmit schedule in a wireless…
We study the problem of wireless sensor network design by deploying a minimum number of additional relay nodes (to minimize network cost) at a subset of given potential relay locations, in order to convey the data from already existing…