Computing the Fréchet distance between folded polygons

Authors:
Atlas F. Cook, IV;Anne Driemel;Sariel Har-Peled;Jessica Sherette;Carola Wenk
Affiliations:
Department of Information and Computing Sciences, University of Utrecht, Netherlands;Department of Information and Computing Sciences, University of Utrecht, Netherlands;Department of Computer Science, University of Illinois;Department of Computer Science, University of Texas at San Antonio;Department of Computer Science, University of Texas at San Antonio
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

Computing the Fréchet 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 Fréchet 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 Fréchet distance in polynomial time.