Weighted sequence graphs: boosting iterated dynamic programming using locally suboptimal solutions

We present a novel technique for improving a fundamental aspect of iterated dynamic programming procedures on sequences, such as progressive sequence alignment. Instead of relying on the unrealistic assumption that each iteration can be performed accurately without including information from other sequences, our technique employs the combinatorial data structure of weighted sequence graphs to represent an exponential number of optimal and suboptimal sequences. The usual dynamic programming algorithm on linear sequences can be generalized to weighted sequence graphs, and therefore allows to align sequence graphs instead of individual sequences in subsequent stages. Thus, locally suboptimal, but globally correct solutions can for the first time be identified through iterated sequence alignment. We demonstrate the utility of our technique by applying it to the benchmark alignment problem of Sankoff et al. (J. Mol. Evol. 7 (1976) 133). Although a recent effort could improve on the original solution from 1976 slightly, our technique leads to even more significant improvements