Zobrazeno 1 - 10
of 34
pro vyhledávání: '"52C15, 52C17"'
Autor:
Rosenbluth, Eran
Various real-world problems consist of partitioning a set of locations into disjoint subsets, each subset spread in a way that it covers the whole set with a certain radius. Given a finite set S, a metric d, and a radius r, define a subset (of S) S'
Externí odkaz:
http://arxiv.org/abs/2302.03451
Autor:
Forst, Maxwell, Fukshansky, Lenny
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry of lattice
Externí odkaz:
http://arxiv.org/abs/2212.08807
Autor:
Tóth, Gábor Fejes
This paper surveys the theory of multiple packings and coverings. The study of multiple arrangements started in the 60s of the last century, and it was restricted mostly to lattice arrangements on the plane or of general arrangements of balls. We emp
Externí odkaz:
http://arxiv.org/abs/2202.11383
Autor:
Tóth, Gábor Fejes
This paper suveys different variants of the following problem: Given a convex set $K$ and a sequence $\{C_i\}$ of convex bodies in $E^n$, is it possible to pack the sequence of bodies in $K$ or cover $K$ with the bodies? Algorithmic versions of these
Externí odkaz:
http://arxiv.org/abs/2202.11379
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 path probl
Externí odkaz:
http://arxiv.org/abs/2202.11366
\textit{Parastichies} are spiral patterns observed in plants and numerical patterns generated using golden angle method. We generalize this method by using Markoff theory and the theory of product of linear forms, to obtain a theory for packing of Ri
Externí odkaz:
http://arxiv.org/abs/2106.12333
We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the problem is s
Externí odkaz:
http://arxiv.org/abs/1705.09346
Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula, to give a
Externí odkaz:
http://arxiv.org/abs/1602.08593
Autor:
Le, Quang-Nhat, Robins, Sinai
The solid-angle sum $A_{\mathcal{P}} (t)$ of a rational polytope ${\mathcal{P}} \subset \mathbb{R}^d$, with $t \in \mathbb{Z}$ was first investigated by I.G. Macdonald. Using our Fourier-analytic methods, we are able to establish an explicit formula
Externí odkaz:
http://arxiv.org/abs/1602.02681
Autor:
Kallus, Yoav, Kusner, Wöden
Publikováno v:
Discrete & Computational Geometry 56:2, 449-471 (2016)
This paper introduces a technique for proving the local optimality of packing configurations. Applying this technique to a general convex polygon, we prove that the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also
Externí odkaz:
http://arxiv.org/abs/1509.02241