We consider the inverse parametric sequence alignment problem, where a sequence alignment is given and the task is to determine parameter values such that the given alignment is optimal at that parameter setting. We describe a O(rnn log m)-time algorithm for inverse global alignment without gaps and a O(rnn log 2 rn) time algorithm for global alignment with gaps, where rn, ( _ rn) are the lengths of input strings. We then discuss algorithms for local alignment.