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

Authors
  • Cook, Atlas F.
  • Driemel, Anne
  • Har-Peled, Sariel
  • Sherette, Jessica
  • Wenk, Carola
Type
Preprint
Publication Date
Mar 15, 2011
Submission Date
Mar 15, 2011
Source
arXiv
License
Yellow
External links

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.

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