Computing the Fréchet distance between simple polygons in polynomial time

Authors:
Kevin Buchin;Maike Buchin;Carola Wenk
Affiliations:
Freie Universität Berlin, Berlin, Germany;Freie Universität Berlin, Berlin, Germany;University of Texas, San Antonio, TX
Venue:
Proceedings of the twenty-second annual symposium on Computational geometry
Year:
2006

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Abstract

We present the first polynomial-time algorithm for computing the Fréchet for a non-trivial class of surfaces: simple polygons. For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths in the other polygon.