Alignment with Non-overlapping Inversions in O(n3)-Time

Alignments of sequences are widely used for biological sequence comparisons. Only biological events like mutations, insertions and deletions are usually modeled and other biological events like inversions are not automatically detected by the usual alignment algorithms. Alignment with inversions does not have a known polynomial algorithm and a simplification to the problem that considers only non-overlapping inversions were proposed by Schöniger and Waterman [20] in 1992 as well as a corresponding O(n) solution. An improvement to an algorithm with O(n log n)-time complexity was announced in an extended abstract [1] and, in this present paper, we give an algorithm that solves this simplified problem in O(n)-time and O(n)-space in the more general framework of an edit graph. Inversions have recently [4, 7, 13, 17] been discovered to be very important in Comparative Genomics and Scherer et al. in 2005 [11] experimentally verified inversions that were found to be polymorphic in the human genome. Moreover, 10% of the 1,576 putative inversions reported overlap RefSeq genes in the human genome. We believe our new algorithms may open the possibility to more detailed studies of inversions on DNA sequences using exact optimization algorithms and we hope this may be particularly interesting if applied to regions around known rearrangements boundaries. Scherer report 29 such cases and prioritize them as candidates for biological and evolutionary studies.