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We present a unified framework for accelerating edit-distance computationbetween two compressible strings using straight-line programs. For two stringsof total length $N$ having straight-line program representations of total size$n$, we provide an algorithm running in $O(n^{1.4}N^{1.2})$ time for computingthe edit-distance of these two strings under any rational scoring function, andan $O(n^{1.34}N^{1.34})$ time algorithm for arbitrary scoring functions. Thisimproves on a recent algorithm of Tiskin that runs in $O(nN^{1.5})$ time, andworks 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 ourSLP edit-distance scheme, giving us a simple $\Omega(\lg N)$ speed-up in thecase of arbitrary scoring functions, for any pair of strings.

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