Edit distance

About: Edit distance is a research topic. Over the lifetime, 2887 publications have been published within this topic receiving 71491 citations.

Recognition of Noisy Subsequences Using Constrained Edit Distances

Abstract: Let X* be any unknown word from a finite dictionary H Let U be any arbitrary subsequence of X* We consider the problem of estimating X* by processing Y, which is a noisy version of U We do this by defining the constrained edit distance between XH and Y subject to any arbitrary edit constraint involving the number and type of edit operations to be performed An algorithm to compute this constrained edit distance has been presented Although in general the algorithm has a cubic time complexity, within the framework of our solution the algorithm possesses a quadratic time complexity Recognition using the constrained edit distance as a criterion demonstrates remarkable accuracy Experimental results which involve strings of lengths between 40 and 80 and which contain an average of 26547 errors per string demonstrate that the scheme has about 995 percent accuracy

A Metric Index for Approximate String Matching

Abstract: We present a radically new indexing approach for approximate string matching. The scheme uses the metric properties of the edit distance and can be applied to any other metric between strings. We build a metric space where the sites are the nodes of the suffix tree of the text, and the approximate query is seen as a proximity query on that metric space. This permits us finding the R occurrences of a pattern of length m in a text of length n in average time O(mlog2 n+m2+R), using O(n log n) space and O(n log2 n) index construction time. This complexity improves by far over all other previous methods. We also show a simpler scheme needing O(n) space.

Evaluating Text Segmentation using Boundary Edit Distance

Abstract: This work proposes a new segmentation evaluation metric, named boundary similarity (B), an inter-coder agreement coefficient adaptation, and a confusion-matrix for segmentation that are all based upon an adaptation of the boundary edit distance in Fournier and Inkpen (2012). Existing segmentation metrics such as Pk, WindowDiff, and Segmentation Similarity (S) are all able to award partial credit for near misses between boundaries, but are biased towards segmentations containing few or tightly clustered boundaries. Despite S’s improvements, its normalization also produces cosmetically high values that overestimate agreement & performance, leading this work to propose a solution.

Approximating edit distance in near-linear time

Abstract: We show how to compute the edit distance between two strings of length n up to a factor of 2(O-tilde(sqrt(log n))) in n(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n(1/3+o(1)) approximation. Previously, approximation of 2O √log n) was known only for embedding edit distance into l1, and it is not known if that embedding can be computed in less than a quadratic time.

Approximating Edit Distance in Near-Linear Time

Abstract: We show how to compute the edit distance between two strings of length n up to a factor of 2^{\~O(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n^(1/3+o(1)) approximation. Previously, approximation of 2^{\~O(sqrt(log n))} was known only for embedding edit distance into l_1, and it is not known if that embedding can be computed in less than quadratic time.