AI 中文总结
本文针对持有长字符串的双方，提出通信高效且低开销的字符串协调与编辑距离算法，在一般及特定场景下实现了更优的通信量与时间开销。
AI 中文摘要
假设双方，Alice和Bob，分别持有长字符串X和Y，他们想要确定X和Y的相似程度，并且希望交换字符串的成本与它们的不相似程度成比例。这类问题出现在数据库与文件系统同步操作、DNA序列比较等场景中。由于字符串较长，当字符串足够相似时，我们关注通信高效且Alice和Bob计算开销低的方法。本文针对此类字符串协调与编辑距离问题，提出了简单低开销且通信高效的算法。在仅假设X和Y的编辑距离存在上界k的一般情况下，我们展示如何以高概率仅使用O(k²log n)比特的通信量和最优的O(n)时间开销来确定X和Y之间的编辑距离k。对于典型英文文本或DNA序列等特定情况，当我们能对输入字符串的分布做出合理的额外假设时，我们展示如何实现更优的界，例如O(k log³ n)比特的通信量。
英文摘要
Suppose two parties, Alice and Bob, hold long character strings, $X$ and $Y$, respectively, and they are interested in determining how similar $X$ and $Y$ are. {Moreover, they want to exchange the strings with cost proportional to their degree of dissimilarity.} Such problems arise, for example, in database and file system synchronization operations, as well as in DNA sequence comparisons. Since the strings are long, we are interested in methods that are communication-efficient and have low overhead in terms of the computations that Alice and Bob must perform, when the strings are similar enough. In this paper, we provide simple low-overhead communication-efficient algorithms for such string reconciliation and edit distance problems. In the general case, %where the only assumption we make is that we have an upper bound, $k$, on the edit distance between $X$ and $Y$, we show how to determine the edit distance $k$ between $X$ and~$Y$ using only $O(k^2\log n)$ bits of communication and optimal $O(n)$ time overhead, with high probability. For specialized cases, such as typical English text or DNA sequences, where we can make additional well-justified assumptions about the distribution of the input strings, we show how to achieve possibly better bounds, such as $O(k\log^5 n)$ bits of communication.
CommentsExtended version of SPIRE'26 paper
