Related papers: Covering a line segment with variable radius discs
An important problem in wireless sensor networks is to find the minimal number of randomly deployed sensors making a network connected with a given probability. In practice sensors are often deployed one by one along a trajectory of a…
This paper investigates coverage control for visual sensor networks based on gradient descent techniques on matrix manifolds. We consider the scenario that networked vision sensors with controllable orientations are distributed over 3-D…
This paper deals with the coverage problem of wireless sensor network. We use the density based clustering technique - OPTICS to cover a target region with less number of sensor nodes. OPTICS works well to identify the outliers, core points…
This thesis focuses on two concepts which are widely studied in the field of computational geometry. Namely, visibility and unit disk graphs. In the field of visibility, we have studied the conflict-free chromatic guarding of polygons, for…
We define the problem segment cover as follows. We are given a set of pairs of sub-intervals of the unit interval. The problem asks if there is a choice of a single interval from each pair such that the union of the chosen intervals covers…
Sensor networks are particularly applicable to the tracking of objects in motion. For such applications, it may not necessary that the whole region be covered by sensors as long as the uncovered region is not too large. This notion has been…
An image line segment is a fundamental low-level visual feature that delineates straight, slender, and uninterrupted portions of objects and scenarios within images. Detection and description of line segments lay the basis for numerous…
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization…
We present an interactive visualization system for exploring the coverage in sensor networks with uncertain sensor locations. We consider a simple case of uncertainty where the location of each sensor is confined to a discrete number of…
In this paper, we propose several regular covers with identical sectors that observe the strip in the same direction, and we carried out their analysis, which allows choosing the best coverage model and the best parameters of the sector.
We consider the problem of decomposing a piecewise constant function on the circle into a sum of indicator functions of closed circular disks in the plane, whose number and location are not a priori known. This represents a situation where…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
This paper presents a solution to the problem of monitoring a region of interest (RoI) using a set of nodes that is not sufficient to achieve the required degree of monitoring coverage. In particular, sensing coverage of wireless sensor…
Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that…
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph $G$, the segment number of $G$ is the minimum number of segments that can be achieved by any planar straight-line…
We study extensions of the classic \emph{Line Cover} problem, which asks whether a set of $n$ points in the plane can be covered using $k$ lines. Line Cover is known to be NP-hard, and we focus on two natural generalizations. The first is…
We consider the problem of deciding, given a sequence of regions, if there is a choice of points, one for each region, such that the induced polyline is simple or weakly simple, meaning that it can touch but not cross itself. Specifically,…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
We present an instance of the optimal sensor scheduling problem with the additional relaxation that our observer makes active choices whether or not to observe and how to observe. We mask the nodes in a directed acyclic graph of the model…