Related papers: Covering a line segment with variable radius discs
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional…
Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…
We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the…
We are interested in the following problem of covering the plane by a sequence of congruent circular disks with a constraint on the distance between consecutive disks. Let $(\mathcal{D}_n)_{n \in \mathbb N}$ be a sequence of closed unit…
With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
We consider the problem where a network of sensors has to detect the presence of targets at any of $n$ possible locations in a finite region. All such locations may not be occupied by a target. The data from sensors is fused to determine…
This paper considers a movement minimization problem for mobile sensors. Given a set of $n$ point targets, the $k$-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at $k$ base stations, to cover…
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
Multirobot systems for covering environments are increasingly used in applications like cleaning, industrial inspection, patrolling, and precision agriculture. The problem of covering a given environment using multiple robots can be…
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
The vertex p-center problem consists of locating p facilities among a set of M potential sites such that the maximum distance from any demand to its closest located facility is minimized. The complete vertex p-center problem solves the…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
The Variable Sized Bin Packing Problem has a wide range of application areas including packing, scheduling, and manufacturing. Given a list of items and variable sized bin types, the objective is to minimize the total size of the used bins.…
In COCOA 2015, Korman et al. studied the following geometric covering problem: given a set $S$ of $n$ line segments in the plane, find a minimum number of line segments such that every cell in the arrangement of the line segments is…
Sensor network localization problem is to determine the position of the sensor nodes in a network given pairwise distance measurements. Such problem can be formulated as a polynomial minimization via the least squares method. This paper…
Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed…
A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. The objective of an agent with known dynamics traversing the region is to identify the true classifier while paying a…