An efficient uniform-cost normalized edit distance algorithm

Abstract

A common model for computing the similarity of two strings X and Y of lengths m, and n respectively with m n, is to transform X into Y through a sequence of three types of edit operations: insertion, deletion, and substitution. The model assumes a given cost function which assigns a non-negative real weight to each edit operation. The amortized weight for a given edit sequence is the ratio of its weight to its length, and the minimum of this ratio over all edit sequences is the normalized edit distance. Existing algorithms for normalized edit distance computation with proven complexity bounds require Omn 2 time in the worst-case. We give an Omn log n-time algorithm for the problem when the cost function is uniform, i.e, the weight of each edit operation is constant within the same type, except substitutions can have different weights depending on whether they are matching or non-matching.

Optimization and Selection of Diagnosis-Oriented Fault-Insertion Points for System Test

“…The most similar error flow is selected from the dictionary, and its corresponding fault is considered to be the root cause of the failure. The similarity of two error flows is evaluated based on the edit distance, a widely used metric in string-matching algorithm [13], [14]. Edit distance is also referred as Levenshtein distance.…”

Grouping Multidimensional Data

“…The last two references also contain material related to string similarity, where biology is one application. For strings over the same alphabet, edit distance is frequently used [25]. Edit distance is based on the length of a sequence of transformations (such as insertion, deletion, transposition, etc.)…”

A new approach to sequence comparison

“…In such cases these values give us the possible candidates for the end-points of the smallest interval which eventually contains the optimum value (ratio). (In some applications, even all candidate optimum values can be precomputed e ciently (Arslan and E gecio glu, 1999;Arslan and E gecio glu, 2000).…”

“…We want to emphasize the di erence between the normalized local alignment and the previously studied normalized edit distance problem. The algorithms by Oommen andZhang (1996), Vidal et al (1995), Arslan and E gecio glu (1999), Arslan and E gecio glu (2000) do not aim to satisfy a constraint on the length, therefore they cannot directly be adapted to the the computation of normalized scores when lengths are restricted.…”

“…In this paper, we propose a new practical algorithm that produces local alignment with maximum degree of similarity by extending the ideas presented by E gecio glu (1999), Arslan andE gecio glu (2000). To re ect the length of the local alignment in scoring, the score s(I; J) of local alignment involving substrings I and J may be adjusted by dividing s(I; J) by the total length of the aligned regions: s(I; J)=(jIj + jJj).…”