A Space Efficient Algorithm for Sequence Alignment with Inversions

Abstract

A dynamic programming algorithm to find an optimal alignment for a pair of DNA sequences has been described by Schöniger and Waterman. The alignments use not only substitutions, insertions, and deletions of single nucleotides, but also inversions, which are the reversed complements, of substrings of the sequences. With the restriction that the inversions are pairwise non-intersecting, their proposed algorithm runs in O(n ² m ²) time and consumes O(n ² m ²) space, where n and m are the lengths of the input sequences respectively. We develop a space efficient algorithm to compute such an optimal alignment which consumes only O(nm) space within the same amount of time. Our algorithm enables the computation for a pair of DNA sequences of length up to 10,000 to be carried out on an ordinary desktop computer. Simulation study is conducted to verify some biological facts about gene shuffling across species.

Supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 14580390. Part of the work done while visiting at University of Alberta.

Corresponding author. Supported in part by NSERC grants RGPIN249633 and A008599, and a REE Startup Grant from the University of Alberta.