Topic
Edit distance
About: Edit distance is a research topic. Over the lifetime, 2887 publications have been published within this topic receiving 71491 citations.
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TL;DR: It is formally shown that the new distance measure is a metric, based on the maximal common subgraph of two graphs, which is superior to edit distance based measures in that no particular edit operations together with their costs need to be defined.
782 citations
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TL;DR: An algorithm is described for computing the edit distance between two strings of length n and m, n ⪖ m, which requires O(n · max(1, mlog n) steps whenever the costs of edit operations are integral multiples of a single positive real number and the alphabet for the strings is finite.
739 citations
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TL;DR: An improved algorithm that works in time and in space O and algorithms that can be used in conjunction with extended edit operation sets, including, for example, transposition of adjacent characters.
Abstract: The edit distance between strings a 1 … a m and b 1 … b n is the minimum cost s of a sequence of editing steps (insertions, deletions, changes) that convert one string into the other. A well-known tabulating method computes s as well as the corresponding editing sequence in time and in space O ( mn ) (in space O (min( m, n )) if the editing sequence is not required). Starting from this method, we develop an improved algorithm that works in time and in space O ( s · min( m, n )). Another improvement with time O ( s · min( m, n )) and space O ( s · min( s, m, n )) is given for the special case where all editing steps have the same cost independently of the characters involved. If the editing sequence that gives cost s is not required, our algorithms can be implemented in space O (min( s, m, n )). Since s = O (max( m, n )), the new methods are always asymptotically as good as the original tabulating method. As a by-product, algorithms are obtained that, given a threshold value t , test in time O ( t · min( m, n )) and in space O (min( t, m, n )) whether s ⩽ t . Finally, different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets, including, for example, transposition of adjacent characters.
672 citations
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06 Jan 1992TL;DR: Two string distance functions that are computable in linear time give a lower bound for the edit distance (in the unit cost model), which leads to fast hybrid algorithms for the edited distance based string matching.
Abstract: We study approximate string matching in connection with two string distance functions that are computable in linear time. The first function is based on the so-called $q$-grams. An algorithm is given for the associated string matching problem that finds the locally best approximate occurences of pattern $P$, $|P|=m$, in text $T$, $|T|=n$, in time $O(n\log (m-q))$. The occurences with distance $\leq k$ can be found in time $O(n\log k)$. The other distance function is based on finding maximal common substrings and allows a form of approximate string matching in time $O(n)$. Both distances give a lower bound for the edit distance (in the unit cost model), which leads to fast hybrid algorithms for the edit distance based string matching.
665 citations
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TL;DR: A novel algorithm is introduced which allows us to approximately, or suboptimally, compute edit distance in a substantially faster way and is emprically verified that the accuracy of the suboptimal distance remains sufficiently accurate for various pattern recognition applications.
654 citations