A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression

Abstract: We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we provide an algorithm running in $O(n<sup>{1.4}N<sup>{1.2})$ time for computing the edit-distance of these two strings under any rational scoring function, and an $O(n<sup>{1.34}N<sup>{1.34})$ time algorithm for arbitrary scoring functions. This improves on a recent algorithm of Tiskin that runs in $O(nN<sup>{1.5})$ time, and works only for rational scoring functions. Also, in the last part of the paper, we show how the classical four-russians technique can be incorporated into our SLP edit-distance scheme, giving us a simple $\Omega(\lg N)$ speed-up in the case of arbitrary scoring functions, for any pair of strings.