Related papers: Exact Cover with light
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
Absorption of electromagnetic energy by a material is a phenomenon that underlies many applied problems, including molecular sensing, photocurrent generation and photodetection. Commonly, the incident energy is delivered to the system…
Visual object recognition under situations in which the direct line-of-sight is blocked, such as when it is occluded around the corner, is of practical importance in a wide range of applications. With coherent illumination, the light…
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each…
We consider a fashion discounter distributing its many branches with integral multiples from a set of available lot-types. For the problem of approximating the branch and size dependent demand using those lots we propose a tailored exact…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
In this paper, we study a class of set cover problems that satisfy a special property which we call the {\em small neighborhood cover} property. This class encompasses several well-studied problems including vertex cover, interval cover,…
A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…
We show theoretically that coherent light can be completely absorbed in a two-dimensional or three-dimensional metallic nanostructure by matching the frequency and field pattern of an incident wave to that of a localized surface plasmon…
In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for…
Given a set of objects with durations (jobs) that cover a base region, can we schedule the jobs to maximize the duration the original region remains covered? We call this problem the sensor cover problem. This problem arises in the context…
The problem of the principal existence of the perfect lens and superlensing is discussed. We have demonstrated that in the case of the virtual focus the idea of perfect lens based upon amplification of evanescent waves as proposed by Pendry…
Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-dimensional matching problem asks whether there is a disjoint collection of the hyperedges which…
The eternal vertex cover problem is a dynamic variant of the classical vertex cover problem. It is NP-hard to compute the eternal vertex cover number of graphs and known algorithmic results for the problem are very few. This paper presents…
The worst-case fastest known algorithm for the Set Cover problem on universes with $n$ elements still essentially is the simple $O^*(2^n)$-time dynamic programming algorithm, and no non-trivial consequences of an $O^*(1.01^n)$-time…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
We study the problem of covering a given point set in the plane by unit disks so that each point is covered exactly once. We prove that 17 points can always be exactly covered. On the other hand, we construct a set of 657 points where an…
This paper discusses the problem of covering and hitting a set of line segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such that the side length of the larger of the two squares is minimized. We also discuss the…