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# 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 $O(n^{1.4}N^{1.2})$ time for computing the edit-distance of these two strings under any rational scoring function, and an $O(n^{1.34}N^{1.34})$ time algorithm for arbitrary scoring functions. This improves on a recent algorithm of Tiskin that runs in $O(nN^{1.5})$ 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.
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https://hal.inria.fr/inria-00360821
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Submitted on : Monday, February 16, 2009 - 10:49:34 AM
Last modification on : Tuesday, August 13, 2019 - 10:50:23 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 8:44:35 PM

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### Identifiers

• HAL Id : inria-00360821, version 1
• ARXIV : 0902.2649

### Citation

Danny Hermelin, Gad M. Landau, Shir Landau, Oren Weimann. A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. pp.529-540. ⟨inria-00360821⟩

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