Computing the Fréchet distance between folded polygons

Computing the Fréchet 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 Fréchet 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 Fréchet distance for L∞L∞ in polynomial time.