Finding Winner Alignments with Multiple Scoring Matrices

How to align two given sequences properly is a fundamental problem in bioinformatics. In the sequence alignment problem, the most essential thing that directly affects the resulting alignment is the scoring matrix. There are a variety of scoring matrices used for alignment, and each of them has its own purpose in biosequence alignment. It seems unlikely that an alignment is optimal for each scoring matrix. But, there may be one that meets the most matrices with acceptable scores. In this paper, we present an efficient algorithm for finding the winner alignment when multiple scoring matrices are applied. We then discuss the variants of the comparing function. By simply reordering the steps in the comparing function, we could obtain another winner alignment under different criterion. Our algorithm solves the problem in O(kmn) time where k is the number of scoring matrices involved, and m and n are the lengths of the two input sequences. A more efficient algorithm with O(k(|Σ|+ 1)2 + mn) time can find the winner alignment under the summing scheme, where |Σ| denotes the alphabet size of the input sequences.