Computing all Suboptimal Alignments in Linear Space

Recently, a new compact representation for suboptimal alignments was proposed by Naor and Brutlag (1993). The kernel of that representation is a minimal directed acyclic graph (DAG) containing all suboptimal alignments. In this paper, we propose a method that computes such a DAG in space linear to the graph size. Let F be the area of the region of the dynamic-programming matrix bounded by the suboptimal alignments and W the maximum width of that region. For two sequences of lengths M and N , it is shown that the worst-case running time is O(MN + F log log W ). To exploit the computed DAG, we employ a variant of Aho-Corasick pattern matching machine (Aho and Corasick, 1975) to locate all occurrences of specified patterns, and then find a path in the DAG that maximizes the sum of the scores of the non-overlapping patterns occurring in it. An example illustrates the utility.