Questions tagged [edit-distance]

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20
votes
2answers
8k views

efficient diff algorithm for trees and Levenshtein distance

I've recently read this summary of the issues involved with doing diff between trees and it got me interested in learning what is the state of the art for this problem. Also, suppose that between ...
19
votes
1answer
730 views

Edit distance in sublinear space

What is the best known complexity for computing the exact edit distance between two strings of the same length using working space which is sublinear in the size of the input? I assume the input is ...
16
votes
3answers
756 views

Edit distance between two partitions

I have two partitions of $[1 \ldots n]$ and am looking for the edit distance between them. By this, I want to find the minimal number of single transitions of a node into a different group that are ...
14
votes
2answers
1k views

Category-theoretic treatment of diffs, patches and merging?

Is there a category of patches that looks roughly like this: The objects are strings in some base alphabet The morphisms are edit scripts ("diffs" or "patches") between the strings I'm interested in ...
13
votes
2answers
875 views

Edit distance with move operations

Motivation: A coauthor edits a manuscript and I would like to see a clear summary of the edits. All "diff"-like tools tend to be useless if you are both moving text around (e.g., re-organising the ...
12
votes
2answers
3k views

Space complexity to compute the optimal string alignment for the Levenshtein edit distance

If we are given two strings of size $n_1$ and $n_2$, the standard Levenshtein edit distance computation is by a dynamic algorithm with time complexity $O(n_1 n_2)$ and space complexity $O(n_1 n_2)$. (...
11
votes
4answers
580 views

Shortest number of editing move between two words

I am looking for a data structure and an algorithm to compute the minimum number of changes required to transform one word into another, given the two words as inputs, where the only allowed changes ...
10
votes
2answers
271 views

Complexity of Homogenizing a String

Motivation: While developing tools for data versioning, we ended up looking into algorithms for "diff"ing two sets of integers, by coming up with a sequence of transformations that take one set of ...
8
votes
4answers
735 views

Intermediate/Coding representation for Levenshtein Distance

The phrases: The quick brown fox jumps over the lazy dog [A] and The uick brown fox jumps oower the lazy dog [B] can be compared using Levenshtein Distance algorithm to determine similarity ...
8
votes
1answer
861 views

Efficiently finding the minimum number of transpositions needed to sort a list

I'd like an efficient method for calculating the minimum number of transpositions needed to sort a list. I don't need to know what the transpositions actually are. For example, the list [1, 1, 2, 0] ...
7
votes
2answers
2k views

Proof of Levenshtein distance

In the article Levenshtein distance Wikipedia says about the proof of invariant that: This proof fails to validate that the number placed in d[i,j] is in fact minimal; this is more difficult to ...
6
votes
1answer
253 views

Find a string with minimal edit distance from a set of given strings

Input: a bunch of binary strings: x_0, x_1, ... , x_n Output: a binary string y that minimizes edit(x_0, y) + edit(x_1, y) + ... edit(x_n, y) where edit(x, y) denotes the levenshtein distance, i.e. ...
4
votes
2answers
912 views

Min Hamming distance of a given string from substrings of another string

Let $U$ be a small finite set. Consider the following problem: Input: two strings $u \in U^k$ and $v\in U^n$ with $k \leq n$. Output: a (contiguous) substring of $v$ of length $k$ with the minimum ...
3
votes
1answer
333 views

Using compression to improve edit distance computation

I am doing a seminar on a paper titled "Unified Compression-Based Acceleration of Edit-Distance Computation" that uses straight-line programs to improve edit distance computation. It is a common ...
3
votes
0answers
73 views

Communication complexity of edit resilient synchronization

Supposing we have two strings $A$ and $B$ that are both edit distance $\tau$ from each other at two different sites is there a communication complexity model where synchronizing such strings have been ...
2
votes
1answer
368 views

Edit distance algorithms that depend on alphabet

The best known algorithm for computing the exact edit distance between two strings is I believe an algorithm by Masek and Paterson that runs in time $O(n^2/\log^2 n)$, for binary alphabets. Is there ...
2
votes
1answer
258 views

Algorithm for computing unordered tree edit distance

I am trying to compute the edit distance between two dendrograms, one produced from hierarchical clustering, and the other manually constructed from some tree structure. In this setting, the rename ...
2
votes
1answer
104 views

Long distance string problem

We are considering length n strings over the alphabet S. The goal is to compute a set of string, M, such that for any string, x, in S^n there exists a string, y, in M such that the hamming distance ...
2
votes
0answers
80 views

Why is triangle inequality needed for indexing?

Maybe this is a silly question but I actually can't fulfill that by myself. I'm reading some papers about similarity metrics and I always find that for a distance function $d$ the triangle inequality ...
2
votes
0answers
376 views

extension for Levenshtein distance

I am looking for an extension for Levenshtein distance (Edit distance) for multi dimensional strings (2D and 3D). I am not sure if there is a formal definition for multi dimensional or not, but here ...
1
vote
1answer
735 views

Spell Checker with BK tree and edit distance that accounts for transpositions

I want to try and write code for a BK tree using a certain edit distance that accounts for transpositions for a spell corrector. I've looked into Damerau-Levenshtein distance, but the triangle ...
1
vote
0answers
51 views

Which algorithms can be used to measure similarity for two very different languages?

recently I have read this paper, A Survey of text similarity approaches, and I discovered that there are a lot of algorithms that can be used to measure similarity. At present I am applying the ...
1
vote
0answers
178 views

Edit-Distance of weighted automata

I'm trying to understand "Edit Distance of Weighted Automata" by Mehryar Mohri: [83], [93] and [99] at http://www.cs.nyu.edu/~mohri/pub/ (they are virtually identical so which of them doesn't matter). ...
0
votes
1answer
66 views

Relation between edit distances over different alphabets

Assume we have two strings $S_1$ and $S_2$ of lengths $cn$ and $cm$ bits resepctively for some $c\in\Bbb N$. Assume that the Levenshtein distance (minimum number of single-character edits (i.e. ...
-1
votes
1answer
137 views

L1 / Variational Distance between distributions [closed]

My statistics knowledge is somewhat poor, so I have to ask one (dumb) question. Let $\beta$ be a real number in the interval $\big[0, \frac{1}{2}\big)$ and $\mathcal{D}_1, \mathcal{D}_2, \mathcal{D}...