The complexity of multiple sequence alignment with SP-score that is a metric

AbstractThis paper analyzes the computational complexity of computing the optimal alignment of a set of sequences under the sum of all pairs (SP) score scheme. We solve an open question by showing that the problem is NP-complete in the very restricted case in which the sequences are over a binary alphabet and the score is a metric. This result establishes the intractability of multiple sequence alignment under a score function of mathematical interest, which has indeed received much attention in biological sequence comparison