An Efficient Linear Space Algorithm for Consecutive Suffix Alignment under Edit Distance (Short Preliminary Paper)

Abstract

We discuss the following variant of incremental edit distance computation: Given strings A and B with lengths m and n, respectively, the task is to compute, in n successive iterations j = n ...1, an encoding of the edit distances between A and all prefixes of B _j..n . Here B _j..n is the suffix of B that begins at its jth character. This type of consecutive suffix alignment [3] is powerful e.g. in solving the cyclic string comparison problem [3]. There are two previous efficient algorithms that are capable of consecutive suffix alignment under edit distance: the algorithm of Landau et al. [2] that runs in O(kn) time and uses O(m + n + k ²) space, and the algorithm of Kim and Park [1] that runs in O((m + n)n) time and uses O(mn) space. Here k is a user-defined upper limit for the computed distances (0 ≤ k ≤ max {m,n}). In this paper we propose the first efficient linear space algorithm for consecutive suffix alignment under edit distance. Our algorithm uses O((m + n)n) time and O(m + n) space.