Related papers: On regular and random two-dimensional packing of c…
We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the…
We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number…
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or…
We consider here the percolation problem in thin films, both in the direction normal to the film and in the direction parallel to the film. We thereby describe here the cross-over between 2D and 3D percolation, which we do on cubic and…
The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly…
In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find…
The task of "relative placement" is to predict the placement of one object in relation to another, e.g. placing a mug onto a mug rack. Through explicit object-centric geometric reasoning, recent methods for relative placement have made…
We extend the results previously published on exact packing dimensions of random recursive constructions to include constructions satisfying commonly occurring conditions. We remove the restrictive assumption that the diameter reduction…
In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest…
In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our…
This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…
Despite great progress in the study of critical percolation on $\mathbb{Z}^d$ for $d$ large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions.…
The paper concerns clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis…