Related papers: Efficient Folding Algorithms for Regular Polyhedra
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian…
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)…
Quadratic programming (QP) underpins real-time robotics by enabling efficient, constrained optimization in state estimation, motion planning, and control. In legged locomotion and manipulation, essential modules like inverse dynamics, Model…
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…
We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the…
In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…
Let P be a polygonal curve in R^d of length n, and S be a point-set of size k. We consider the problem of finding a polygonal curve Q on S such that all points in S are visited and the Fr\'echet distance from $P$ is less than a given…
We study on-line strategies for solving problems with hybrid algorithms. There is a problem Q and w basic algorithms for solving Q. For some lambda <= w, we have a computer with lambda disjoint memory areas, each of which can be used to run…
The composite $L_q~(0<q<1)$ minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
In this paper, we have examined the problem of embedding a cycle of n vertices onto a given set of n points inside a simple polygon. The goal of the problem is that the cycle must be embedded without bends and does not intersect itself and…
On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair of coprime integers $(p,q)$ it was found the numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ and satisfying the…
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…
Recent LLM-driven discoveries have renewed interest in geometric packing problems. In this paper, we study several classes of such packing problems through the lens of modern global nonlinear optimization. Starting from comparatively direct…
Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…