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:  This yields an independent proof of 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.