Related papers: Covering a line segment with variable radius discs
In this paper, a deformable object is considered for cameras deployment with the aim of visual coverage. The object contour is discretized into sampled points as meshes, and the deformation is represented as continuous trajectories for the…
A belt region is said to be k-barrier covered by a set of sensors if all paths crossing the width of the belt region intersect the sensing regions of at least k sensors. Barrier coverage can be achieved from a random initial deployment of…
We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity…
Imagine a polygon-shaped platform $P$ and only one static spotlight outside $P$; which direction should the spotlight face to light most of $P$? This problem occurs in maximising the visibility, as well as in limiting the uncertainty in…
We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every straight line passing through S. In spite of its simplicity,…
We settle the pseudo-polynomial complexity of the Demand Strip Packing (DSP) problem: Given a strip of fixed width and a set of items with widths and heights, the items must be placed inside the strip with the objective of minimizing the…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
We show that a $k$-fold covering using translates of an arbitrary convex polygon can be decomposed into $\Omega(k)$ covers (using an efficient algorithm). We generalize this result to obtain a constant factor approximation to the sensor…
Wireless rechargeable sensor networks, consisting of sensor nodes with rechargeable batteries and mobile chargers to replenish their batteries, have gradually become a promising solution to the bottleneck of energy limitation that hinders…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of…
We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the…
Path planning for robotic coverage is the task of determining a collision-free robot trajectory that observes all points of interest in an environment. Robots employed for such tasks are often capable of exercising active control over…
In this paper we study the dynamic aspects of the coverage of a mobile sensor network resulting from continuous movement of sensors. As sensors move around, initially uncovered locations are likely to be covered at a later time. A larger…
This paper addresses optimal feedback selection for generic arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a structured system and a feedback cost matrix, our aim is to find a…