通过文本压缩加速编辑距离计算的统一算法
A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression
摘要：
我们提出了一个统一的框架，用于加速两个可压缩字符串之间的编辑距离计算使用直线程序。对于两个字符串的总长度$N$具有直线程序表示的总大小$n$，我们提供了一个算法运行在$O(n^{1.4}N^{1.2})$时间计算编辑距离的这两个字符串下的任何合理的评分功能，和$O(n^{1.34}N^{1.34})$时间算法的任意评分功能。这改进了Tiskin最近的算法，该算法在$O(nN^{1.5})$时间内运行，并且仅适用于有理评分函数。此外，在本文的最后部分，我们展示了如何将经典的四俄罗斯技术纳入我们的SLP编辑距离方案中，为任意评分函数的情况下提供简单的$Ω(\lg N)$加速，对于任何一对字符串。
英文摘要：
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 $Ω(\lg N)$ speed-up in the case of arbitrary scoring functions, for any pair of strings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
