Before revision:  Our result generalizes an earlier result by Bulteau et al. from 2018 for a variant of DTW that uses squared distances . Moreover, closing some gaps in the literature, we show positive results for a variant where the center curve may have complexity at most \ell under the discrete Fr\'echet distance.
After revision:  Our result generalizes an earlier result by Bulteau et al. from 2018 for a variant of DTW that uses squared distances , where the new proof is both simpler and more general. On the positive side, we give approximation algorithms for problem variants where the center curve may have complexity at most \ell under the discrete Fr\'echet distance.