Related papers: Miscellaneous problems about packing and covering
Order picking and order packing entail retrieving items from storage and packaging them according to customer requests. These activities have always been the main concerns of the companies in reducing warehouse management costs. This paper…
This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.
In the paper we present two examples of inductively free sporadic simplicial arrangements of 31 lines that are non-isomorphic, which allow us to answer negatively questions on the containment problem recently formulated by Drabkin and…
We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.
How can we understand the origins of highly symmetrical objects? One way is to characterize them as the solutions of natural optimization problems from discrete geometry or physics. In this paper, we explore how to prove that exceptional…
We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
When studying the causal propagation of a field in a globally hyperbolic spacetime M, one often wants to express the physical intuition that it has compact support in spacelike directions, or that its support is a spacelike compact set. We…
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…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
We study the well-known Vertex Cover problem parameterized above and below tight bounds. We show that two of the parameterizations (both were suggested by Mahajan, Raman and Sikdar, J. Computer and System Sciences, 75(2):137--153, 2009) are…
We discuss the existence of complete accumulation points of sequences in products of topological spaces. Then we collect and generalize many of the results proved in Parts I, II and IV. The present Part VI is complementary to Part V to the…
In this paper, we study stability for harmonic foliations on locally conformal K\"ahler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact…
We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…
Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for…
In the recent paper \cite{BDT10} we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a "good and fast" packing or…
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…