Approximating Edit Distance Efficiently

Edit distance has been extensively studied for the past several years. Nevertheless, no linear-time algorithm is known to compute the edit distance between two strings, or even to approximate it to within a modest factor. Furthermore, for various natural algorithmic problems such as low-distortion embeddings into normed spaces, approximate nearest-neighbor schemes, and sketching algorithms, known results for the edit distance are rather weak. We develop algorithms that solve gap versions of the edit distance problem: given two strings of length n with the promise that their edit distance is either at most k or greater than , decide which of the two holds. We present two sketching algorithms for gap versions of edit distance. Our first algorithm solves the k vs. (kn)2/3 gap problem, using a constant size sketch. A more involved algorithm solves the stronger k vs. gap problem, where can be as small as O(k2 )--still with a constant sketch--but works only for strings that are mildly "...

• Type: Conference
• Year: 2004
• Where: FOCS
• Authors: Ziv Bar-Yossef, T. S. Jayram, Robert Krauthgamer, Ravi Kumar
• Keywords: Algorithm, Edit Distance, Edit Distance Problem, FOCS 2004, Theoretical Computer Science