Linear space string correction algorithm using the Damerau-Levenshtein distance

The Damerau-Levenshtein (DL) distance metric has been widely used in the biological science. It tries to identify the similar region of DNA,RNA and protein sequences by transforming one sequence to the another using the substitution, insertion, deletion and transposition operations. Lowrance and Wagner have developed an O(mn) time O(mn) space algorithm to find the minimum cost edit sequence between strings of length m and n, respectively. In our previous research, we have developed algorithms that run in O(mn) time using only O(s∗min{m,n}+m+n) space, where s is the size of the alphabet comprising the strings, to compute the DL distance as well as the corresponding edit sequence. These are so far the fastest and most space efficient algorithms. In this paper, we focus on the development of algorithms whose asymptotic space complexity is linear.

We develop linear space algorithms to compute the Damerau-Levenshtein (DL) distance between two strings and determine the optimal trace (corresponding edit operations.)Extensive experiments conducted on three computational platforms-Xeon E5 2603, I7-x980 and Xeon E5 2695-show that, our algorithms, in addition to using less space, are much faster than earlier algorithms.

Besides using less space than the previously known algorithms,significant run-time improvement was seen for our new algorithms on all three of our experimental platforms. On all platforms, our linear-space cache-efficient algorithms reduced run time by as much as 56.4% and 57.4% in respect to compute the DL distance and an optimal edit sequences compared to previous algorithms. Our multi-core algorithms reduced the run time by up to 59.3% compared to the best previously known multi-core algorithms.