Abstract
Given two strings, X and Y, both of length O(n) over alphabet Σ, a basic problem (local alignment) is to find pairs of similar substrings, one from X and one from Y. For substrings X' and Y' from X and Y, respectively, the metric we use to measure their similarity is normalized alignment value: LCS(X',Y')/(|X'|+|Y'|). Given an integer M we consider only those substrings whose LCS length is at least M. We present an algorithm that reports the pairs of substrings with the highest normalized alignment value in O(n log|Σ|+rM log log n) time (r—the number of matches between X and Y). We also present an O(n log|Σ|+rL log log n) algorithm (L = LCS(X,Y)) that reports all substring pairs with a normalized alignment value above a given threshold.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Efraty, N., Landau, G. Sparse Normalized Local Alignment. Algorithmica 43, 179–194 (2005). https://doi.org/10.1007/s00453-005-1152-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-005-1152-3