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Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…
We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super…
We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…
Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories…
We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lov\'asz theta number to Cayley graphs on the special orthogonal group…
The unrestricted block relocation problem is an important optimization problem encountered at terminals, where containers are stored in stacks. It consists in determining the minimum number of container moves so as to empty the considered…
The hypercube queueing model was initially developed to address spatial queueing problems and has found wide applications in emergency services, such as ambulance and police systems. While the model was originally designed for homogeneous…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
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,…
In rectangle packing problems we are given the task of placing axis-aligned rectangles in a given plane region, so that they do not overlap with each other. In Maximum Weight Independent Set of Rectangles (MWISR), their position is given…
Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize…
We give an asymptotic approximation scheme (APTAS) for the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height $1+\gamma$, for some arbitrarily small…
This work proposes a method for effectively computing manipulation paths to rearrange similar objects in a cluttered space. The solution can be used to place similar products in a factory floor in a desirable arrangement or for retrieving a…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
The problem of packing smaller objects within a larger object has been of interest since decades. In these problems, in addition to the requirement that the smaller objects must lie completely inside the larger objects, they are expected to…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container…
In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding…
We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between $n$ objects, and the goal is to find a {\em circular order} of the objects in a manner that is consistent with their dissimilarity.…