Sequence alignments in the neighborhood of the optimum with general application to dynamic programming

When applying dynamic programming techniques to obtain optimal sequence alignments, a set of weights must be assigned to mismatches, insertion/deletions, etc. These weights are not predetermined, although efforts are being made to deduce biologically meaningful values from data. In addition, there are sometimes unknown constraints on the sequences that cause the "true" alignment to disagree with the optimum (computer) solution. To assist in overcoming these difficulties, an algorithm has been developed to produce all alignments within a specified distance of the optimum. The distance can be chosen after the optimum is computed, and the algorithm can be repeated at will. Earlier algorithms to solve this problem were very complex and not practical for any case involving sequences with significant time or storage requirements. The algorithm presented here overcomes these difficulties and has application to general, discrete dynamic programming problems.