Treffer: Approximate unions of lines and minkowski sums

Title:
Approximate unions of lines and minkowski sums
Authors:
VAN KREVELD, Marc, VAN DER STAPPEN, A. Frank
Source:
Twelfth Annual European Symposium on AlgorithmsAlgorithmica. 45(1):91-107
Publisher Information:
New York, NY: Springer, 2006.
Publication Year:
2006
Physical Description:
print, 25 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme approximation, Approximation algorithm, Algoritmo aproximación, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Erreur approximation, Approximation error, Error aproximación, Méthode cas pire, Worst case method, Método caso peor, Métrique Minkowski, Minkowski metric, Métrico Minkowski, Polygone, Polygon, Polígono, Région intérêt, Interest region, Región interès, Algorithms, Approximation, Combinatorial complexity, Minkowski sums
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Institute of Information and Computing Sciences, Utrecht University, 3508 TB Utrecht, Netherlands
ISSN:
0178-4617
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17872486
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.17872486
Database:
PASCAL Archive

Weitere Informationen

We study the complexity of, and algorithms to construct, approximations of the union of lines and of the Minkowski sum of two simple polygons. We also study thick unions of lines and Minkowski sums, which are inflated with a small disc. Let b = D/ε be the ratio of the diameter of the region of interest and the maximum distance (or error) of the approximation. An approximate union of lines or Minkowski sum has complexity Θ(b2) in the worst case. The thick union of n lines has complexity Q(n + b2) and O(n + bbn), and thick Minkowski sums have complexity Ω(n2 + b2) and O((n + b)nb log n + n2 log n) in the worst case. We present algorithms that run in O(n+n2/3+δb4/3) and O(min(bn, n4/3+δb2/3)) time (any δ > 0) for approximate and thick arrangements. For approximate Minkowski sums, the running time is O(min(b2n, n2 + b2 + (nb)4/3+δ)); thick Minkowski sums take O(n8/3+δb2/3) time to compute.