Computing the Fréchet distance between folded polygons

Abstract Computing the Frechet distance for surfaces is a surprisingly hard problem and the only known polynomial-time algorithm is limited to computing it between flat surfaces. We study the problem of computing the Frechet distance for a class of non-flat surfaces called folded polygons. We present a fixed-parameter tractable algorithm for this problem. Next, we present a polynomial-time approximation algorithm. Finally, we present a restricted class of folded polygons for which we can compute the Frechet distance for L ∞ in polynomial time.

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