English

Computing the Fr\'{e}chet Distance Between Folded Polygons

Computational Geometry 2011-03-16 v1

Abstract

Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet distance for a class of non-flat surfaces which we call folded polygons. Unfortunately, the original algorithm cannot be extended directly. We present three different methods to adapt it. The first of which is a fixed-parameter tractable algorithm. The second is a polynomial-time approximation algorithm. Finally, we present a restricted class of folded polygons for which we can compute the Fr\'{e}chet distance in polynomial time.

Keywords

Cite

@article{arxiv.1103.2865,
  title  = {Computing the Fr\'{e}chet Distance Between Folded Polygons},
  author = {Atlas F. Cook and Anne Driemel and Sariel Har-Peled and Jessica Sherette and Carola Wenk},
  journal= {arXiv preprint arXiv:1103.2865},
  year   = {2011}
}

Comments

19 pages, 10 figures. Submitted to WADS 2011

R2 v1 2026-06-21T17:39:35.097Z