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All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in R^d under polyhedral distance functions (e.g., L_1 and L_∞). We also get adoi:10.1007/s00454-016-9800-8 fatcat:okpbqvy7tvgqvlqbr76jimuyli