Reduced space sequence alignment

Motivation: Sequence alignment is the problem of finding theoptimal character-by-character correspondence between two sequences.It can be readily solved in O(n²) time and O(n²) space on aserial machine, or in O(n) time with O(n) space per O(n) processingelements on a parallel machine. Hirschberg's divide-and-conquerapproach for finding the single best path reduces space useby a factor of n while inducing only a small constant slowdownto the serial version. Results: This paper presents a family of methods for computingsequence alignments with reduced memory that are well suitedto serial or parallel implementation. Unlike the divide-and-conquerapproach, they can be used in the forward-backward (Baum-Welch)training of linear hidden Markov models, and they avoid data-dependentrepartitioning, making them easier to parallelize. The algorithmsfeature, for an arbitrary integer L, a factor proportional toL slowdown in exchange for reducing space requirement from O(n²)to O(n). A single best path member of this algorithm familymatches the quadratic time and linear space of the divide-and-conqueralgorithm. Experimentally, the O(n1.5)-space member of the familyis 15–40% faster than the O(n)-space divide-and-conqueralgorithm. Availability: The methods will soon be incorporated in the SAMhidden Markov modeling package http: //www.cse.ucs-c.edu/research/compbio/sam.html. Contact: wzrph{at}cse.ucsc.edu