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Questions tagged [edit-distance]

The edit distance (also: Levenshtein distance) between two strings measures the number of insertions and deletions it takes to convert one string to another.

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Reccomend a textbook which would be useful for developing a spell-checker or static search engine

Suppose that you are working on a search engine for a grocery store self-check-out-machine. If the end-user (human) types the string “green onions” into the check-out-machine, then green onions ...
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Computing similarity of two graphs with partially overlapping sets of nodes

Consider two graphs $G_1 = (E_1, V_1) $ and $G_2 = (E_2, V_2)$ with their associated sets of edges $E$ and nodes $V$. I'm familiar with concepts such as edit distance for computing the similarity/...
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Edit distance between all word pairs

Let there be a dictionary of M words with average length N. We want to compute an M×M matrix of edit distances between all word pairs. Since there are M² word pairs, and the pairwise edit distance ...
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Number of strings at given edit distance

I would like to know the number of strings at edit distance $n$ of a string $s$. I guess this is textbook knowledge... but I cannot find the textbook in question. More formally, I have an alphabet $\...
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187 views

Interleave two arrays such that collisions are minimised (dynamic programming) [closed]

This is a fascinating bioinformatics dynamic programming that I am solving. I am not looking for an answer to the problem, but rather any algorithms, research papers, or other pointers that could be ...
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128 views

Edit Distance Algorithm (variant of longest common sub-sequence)

I'm working on a school assignment which is defined as a variant of the longest common subsequence problem and which is presented in the context of dynamic programming. The problem is defined as ...
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46 views

Graph Edit Distance

Source: K. Riesen, Structural Pattern Recognition with Graph Edit Distance, Advances in Computer Vision and Pattern Recognition. Link: https://www.springer.com/cda/content/document/...
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Can we compute edit distance in strongly sub-quadratic time?

Can we compute the edit distance between two strings of length $n$ in strongly sub-quadratic time, i.e., in time $O(n^{2−\epsilon})$ for some $\epsilon>0$?
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Edit distance for huge strings with bounds

My question is simple but I don't know if the answer is. If you have two strings of length 10 million each, is there an algorithm that would allow you in practice to compute their edit distance (...
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33 views

Non-discrete edit distance for range maps

I'm looking for some kind of edit distance measure between what may be called 'non-discrete symbols sequences'. By a discrete symbol sequence I would mean something like a string, where each symbol ...
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1answer
39 views

Is there a heuristic or function to determine if two arrays of integers are alike or similar

What I am trying to do is determine "closeness" or how similar are arrays of integers (or byte arrays, doesn't matter). For example, let's say a = [0, 1, 2, 3, 4], <...
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How do iterative algorithms for Levenshtein edit distance actually find the number of substitutions, deletions etc.?

Please can someone explain how Levenshtein edit distance works? I've stepped through the algorithm in code and in excel, but I don't understand how this actually succeeds in finding an edit distance. ...
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Is Levenshtein algorithm efficient for text similarity?

I searched on the net the different measures of text similarity. And I found many algorithms concerning this issue and there are classified into many categories such: Token-Based Measure: Tf-idf, ...
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154 views

Extending ordered tree edit distance to DAGs

Computing edit distance (shortest sequence of edit operations) on ordered trees is a well studied problem with many known algorithms (e.g. Zhang & Shasha, RTED). There is also considerable ...
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876 views

Detailed explanation about Damerau Levenshtein Distance algorithm? [closed]

I'm a fresh year Computer Science student. Our teacher gave us damerau levenshtein distance algorithm pseudo code (which he got from Wikipedia apparently) and asked us to explain how the algorithm ...
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89 views

String edit distance between strings x, y, with restrictions on 'intermediary' strings

This is a problem I encountered in a recent interview test. I achieved a slow-ish solution to it, and I'm keen to figure out the most efficient. Problem Given a starting string $x$, a target string ...
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52 views

Regular Expression Metric space

With Levenshtein distance we can create a metric space over string. Is there are any distance metrics for regular expressions?
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943 views

Efficient algorithm for edit distance for short sequences

I have an application that needs to compute billions of levenshtein distance between pairs of strings. The strings are short (70 in length) DNA sequences, consisting only of 4 characters. Also it can ...
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Tracking Solution with Multiple Matrices in Dynamic Programming

We recently figured out a Dynamic Programming solution to compare two trees using concepts of edit distance in strings. It goes something like this- $A[i', i, j', j] = \min \begin{cases} B[i', i-1, ...
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349 views

hamming distance of bloom filters

In the introduction of Distance-Sensitive Bloom Filters the authors state: The relative Hamming distance between two Bloom filters (of the same size, and created with the same hash functions) can ...
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187 views

Complexity of Block edit distance with Swapping only

Suppose I have distinct letters in an alphabet $\sum = \{a_1,a_2,...,a_n\}$. I also have two permutations of these letters, let's call them $A,B$. How can I find the Edit distance between $A$ and $B$ ...
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227 views

Tips for improving implementation of Wagner-Fischer-algorithm

So I'm working on an implementation of a Wagner-Fischer-Algorithm for an online programming challenge site, but I can't seem to push the time down to where it needs to be. The assignment is to, for a ...
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Sequence Alignment with general gap penalties: proof of optimal substructure

I am very well-aware of how optimal substructure for pairwise global sequence alignment using the Needleman-Wunsch algorithm works. However, I have merely seen hand-waving explanations for the ...
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Insert-only Levenshtein distance

I am wondering if a constrained insert-only form of Levenshtein distance has been implemented before by someone? In my particular use case, all other operations should not count as they are not ...
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Advice needed. NLP and ML. Where to start? [closed]

Hi fellow computer scientists, I just began my journey to the world of ML and NLP so please bear with me. I'm hoping to find some guidance here. I would be very grateful if anyone could point me in ...
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What is the error when using Levenshtein distance on flattened binary trees?

I need to calculate the edit distance between many pairs of binary trees. Unfortunately this is computationally expensive. The trees are stored as a flattened list of indices into node and terminal ...
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Find member of CFL that is Levenshtein-closest to non-member string

Is there an (efficient?) algorithm which given a context-free language $L$ (given as a grammar) and a string $x$ with $x \not \in L$ computes a $y$ with $y \in L$ and $\forall y': y' \in L \implies d(...
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87 views

Length of an Edit Script and the Number of Deletions

I am reading the 1989 paper called "An O(NP) Sequence Comparison Algorithm" by Wu, Manber, Myers, and Miller. The algorithm sounds like a good fit for a project I'm doing at work. I have found some ...
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Find all pairs of strings in a set with Levenshtein distance < d

I have a set of $n = $ 100 million strings of length $l = 20$, and for each string in the set, I would like to find all the other strings in the set with Levenshtein distance $\le d = 4$ from that ...
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107 views

Can anybody suggest some algorithms for computing the edit distance other than ‎Wagner–Fischer algorithm? [closed]

I'm currently working with finding edit distance between two string of unequal length. But I'm sorry to say that I've got only one algorithm using Dynamic programming to find out edit distance. But I'...
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284 views

Variation to edit distance depending on position still a metric?

The edit distance between two strings $d(w_1, w_2)$ sums up the cost of edit operations that transform one string into the other. If done right, the edit distance is a metric. In particular, the ...
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193 views

How does Lucene build its inverted index so rapidly

I am writing a small Ruby on Rails engine that does simple full-text search. When someone imports text from a given model (eg. Articles, Posts, etc) an inverted index is built that looks like the ...
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Matching strings in one set to strings in another based on Levenshtein distance

Suppose I have two sets, A and B, which each have one or more strings. I'm looking for an algorithm that'll go through each ...
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What are some efficient ways to find the differences between two large corpuses of text that have similar, but differently ordered content?

I have two large files containing paragraphs of English text: The first text is about 200 pages long and has about 10 paragraphs per page (each paragraph is 5 sentences long). The second text ...
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How to speed up process of finding duplicates/similar items in a large amount of strings?

Our software receives documents (in the order of tens of thousands) from various providers, each document flows through a number of steps, one of those steps finds duplicates and similar documents (...
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855 views

Edit distance between two strings

If X denotes the length of string s1 and Y denotes the length of the string s2, then the edit distance between s1 and s2 is never more than Min(X,Y) or ...
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How to find close match of levenshtein distance [duplicate]

Let's say we have some function, float distance(String a, String b) { /*...*/ } to find the Levenshtein distance between two strings, and we have a large array ...
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Edit distance of list with unique elements

Levenshtein-Distance edit distance between lists is a well studied problem. But I can't find much on possible improvements if it is known that no element does occurs more than once in each list. ...
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105 views

How is the Varshamov-Tenegolts code decoded?

For $0 \leq a \leq n$ the VT code $VT_a(n)$ consists of all tuples $(x_1,x_2,..,x_n) \in \{ 0,1\}^n$ such that $ \sum_{i=1}^{n} ix_i = a (mod (n+1))$ For example $VT_0(4) = \{ 0000,1001,0110,1111 \}$ ...
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Why can't edit distance be solved as L1 distance?

Given two strings $x$ and $y$ over the alphabet $\Sigma$ one defines the edit-distance $\text{ed}(x,y)$ as the minimum number of substitutions, insertions and deletions of characters required to ...
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Sequence alignment with one to many characters

I'm trying to align a sequence of characters together, I found that sequence alignment algorithms which use dynamic programming like Needleman-Wunsch or Smith–Waterman only align one character with ...
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1answer
383 views

Skienna's recursive algorithm for edit distance

I'm having some trouble understanding part of Skienna's algorithm for edit distance presented in his Algorithm Design Manual. I'm posting the recursive version, prior to when he applies dynamic ...
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119 views

Understanding the heuristic used for approximate string searching through an FSA

The paper I'm looking at: Fast approximate string matching with finite automata (2009) Explanation of the algorithm (from my understanding anyway): A word is inputted into the automaton and from ...
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Why is the running time of edit distance with memoization $O(mn)$?

I understand without memoization it is going to be $O(3^{\max\,\{m,n\}})$ because every call results in extra three calls: thus we end up having a call tree with three children for each node, with ...
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Edit distance (Levenshtein-Distance) algorithm explanation

I want to calculate the edit distance (aka Levenshtein-Distance) between two words: «solo» and «oslo». According to this site we'll get the result matrix: What I don't understand is: In case of ...
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How fast can we identifiy almost-duplicates in a list of strings?

I'm having trouble figuring out the upper bound running time for this scenario: Input: $N$ number of strings $M$ upper bound of string length $T$ threshold for edit distance (2 strings with a ...
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Is there a basic proof that there exists some edit distance between two strings?

Title says it all pretty much. I do realize that often edit distance is defined as the minimum number of operations needed to transform one string to another, but I want something to point to that's ...
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565 views

Distance preserving projection for Euclidean distance

Suppose I have two vectors $V_1, V_2 \in R^l$. Can they be converted into bit vectors $B_1,B_2 \in \{0,1\}^l $ such that if $V_1, V_2$ is close in Euclidean distance, $B_1,B_2$ is close in hamming ...
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Semi-local Levenshtein distance

If you have a long string of length $n$ and a shorter string of length $m$, what is a suitable recurrence to let you compute all $n-m+1$ Levevenshtein distances between the shorter string and all ...
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Levenstein distance and dynamic time warp

I am not sure how to draw parallel between the Wagner–Fischer algorithm and dtw algo. In both case we want to find the distance of each index combination (i,j). In Wagner–Fischer, we initiate the ...