Document Open Access Logo

Approximate Shortest Distances Among Smooth Obstacles in 3D

Authors Christian Scheffer, Jan Vahrenhold



PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2016.60.pdf
  • Filesize: 0.54 MB
  • 13 pages

Document Identifiers

Author Details

Christian Scheffer
Jan Vahrenhold

Cite AsGet BibTex

Christian Scheffer and Jan Vahrenhold. Approximate Shortest Distances Among Smooth Obstacles in 3D. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 60:1-60:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ISAAC.2016.60

Abstract

We consider the classic all-pairs-shortest-paths (APSP) problem in a three-dimensional environment where paths have to avoid a set of smooth obstacles whose surfaces are represented by discrete point sets with n sample points in total. We show that if the point sets represent epsilon-samples of the underlying surfaces, (1 ± O(sqrt{epsilon}))-approximations of the distances between all pairs of sample points can be computed in O(n^{5/2} log^2 n) time.
Keywords
  • Geodesic distances; approximation algorithm; epsilon sample

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail