Related papers: Packing ellipsoids with overlap
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…
Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…
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…
We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…
This research concerns a type of configuration optimization problems frequently encountered in engineering design and manufacturing, where the envelope volume in space occupied by a number of components needs to be minimized along with…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in $(0,1]$, and a partition matroid over the items. The goal is to pack all items in a minimum number of unit-size bins, such that…
We study shared multi-processor scheduling problem where each job can be executed on its private processor and simultaneously on one of many processors shared by all jobs in order to reduce the job's completion time due to processing time…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants,…