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

By Atlas F. Cook IV, Anne Driemel, Sariel Har-Peled, Jessica Sherette and Carola Wenk

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.Comment: 19 pages, 10 figures. Submitted to WADS 201

Topics: Computer Science - Computational Geometry
Year: 2011
OAI identifier: oai:arXiv.org:1103.2865
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