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.
This work has been supported by the National Science Foundation grant NSF CAREER CCF-0643597.
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© 2011 Springer-Verlag Berlin Heidelberg
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Cook, A.F., Driemel, A., Har-Peled, S., Sherette, J., Wenk, C. (2011). Computing the Fréchet Distance between Folded Polygons. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_23
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DOI: https://doi.org/10.1007/978-3-642-22300-6_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22299-3
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