# Questions tagged [string-matching]

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### Rabin–Karp vs Karp–Rabin

The wise other editors at Wikipedia have declined my request to move the Wikipedia article on the Rabin–Karp algorithm to what I think it should be called, the Karp–Rabin algorithm, on the basis that ...
6k views

### Computing the Levenshtein distance quickly

Given a huge database of allowed words (alphabetically sorted) and a word, find the word from the database that is closest to the given word in terms of Levenshtein distance. The naive approach is, ...
1k views

### n-dimensional pattern matching

What are some known results for finding an exact n-dimensional subarray inside a n-dimensional array? In 1D, it is just a string matching problem, KMP does it in linear time. In 2D, this paper shown ...
909 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 ...
360 views

### Covering string by palindromes

Given a string $w=\sigma_1\sigma_2\ldots\sigma_n$, a palindrome cover is a sequence $p_1p_2\cdots p_m$ of words $p_i$ such that $p_1p_2\cdots p_m = w$ and such that each $p_i$ is a palindrome. How ...
988 views

### Fibonacci words

I came across the following problem in my old Czech algorithm textbook, sadly came with no hints or solution. "We define Fibonacci words as $F_{0}=a$, $F_{1}=b$, $F_{n+2}=F_{n}F_{n+1}$, where $a$ and ...
273 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 ...
740 views

282 views

### Fast algorithm for scoring a sequence

Let us define: $U = \left\{ u_j \right\}, 1 \leq j \leq N = 2^{L}$, the set of all different binary sequences of length $L$. $V = \left\{ v_i \right\}, 1 \leq i \leq M = \binom{L}{k}2^{k}$, the set ...
342 views

### How to calculate this string-dissimilarity function efficiently?

Migrated from stackoverflow. Hello, I was looking for a string metric that have the property that moving around large blocks in a string won't affect the distance so much. So "helloworld" is close ...
714 views

### Can two strings be matched as disjoint subsequences of a string?

Consider a fixed finite alphabet $A$. I am given as input two strings $S_1$ and $S_2$ on $A$, and a string $S$ on $A$. It is of course possible in PTIME to determine whether $S_1$ is a (non-contiguous)...
84 views

### Fixed-parameter tractability of string homomorphism

String homomorphism is a function $h: \Sigma \to \Sigma^*$, which naturally defines a homomorphism on strings from $\Sigma^*$ with respect to concatenation. We denote $H(s) = h(s_1)h(s_2)\dots h(s_n)$ ...
154 views

### Most frequent $aXa$ substring

Let $s\in\Sigma^*$ be a string, for some alphabet $\Sigma$. We want to find the most frequent repeated substring $q$ of $s$ such that its first character equals its last one, i.e. the most frequent ...
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 ...
133 views

### What is the standard name for the function which inflates a string by duplicating each of its characters?

Given a string $s$ over some alphabet, I'd like to use the proper nomenclature/notation for the operation/function $f$ which inflates $s$ by independently duplicating each of its characters. For ...
94 views

### Find shortest prefix to generate original string by overlapping

Given a string $S$, I want to find the prefix string $P$ of shortest length, such that the original string $S$ can be generated by concatenating copies of $P$ (where overlapping is allowed). For ...
295 views

### Complexity of ambiguous parsing?

Consider the following problem. We are given a set of words $W \subseteq \Sigma^*$ and a set of sentences $S \subseteq W^*$. The "ambiguous parsing" problem consists, given a word $w \in \Sigma^*$, to ...
296 views

### Matching substrings within two strings

I'm currently thinking about the following problem: Given two strings $S,T$ over an alphabet $\Sigma$, return back a list $L$ of common substrings described by their length and positions within them. ...
253 views

### BWT: is it possible to predict the next character in a sequence?

A very simple questions. Let B be the BWT (Burrows–Wheeler transform) of a string S. My question is, due to "grouping" of consecutive characters in BWT, is it possible to somehow know the number of ...
510 views

### Why does the construction step of Aho-Corasick take linear time in the number of nodes?

The original paper's analysis of this, as far as I can tell is this: "THEOREM 3. Algorithm 2 requires time linearly proportional to the sum of the lengths of the keywords. PROOF. Straightforward." ...
148 views

### The edit distance of BWT of two strings with one difference

Let $BWT$ stand for the Burrows-Wheeler transform on strings. What is the maximal edit distance of $BWT(w)$ and $BWT(u)$, if $w$ and $u$ differ only in one character.
833 views

### Algorithm: Find the first k longest substrings between two similar strings

Consider two strings, S and T. Find the first k longest common non-overlapping substrings of S and T.
78 views

### polytime transformation from a graph to a set of binary strings

$d_H$ denotes the Hamming distance between two binary strings of the same size. The problem is stated as follows. Given any undirected graph $(V, A)$, does there always exist a one-to-one ...
285 views

### Algorithm to merge two incomplete sequences of symbols (strings) into a complete one

I initially considered this problem trivial, but then looked with more attention, I could not find an easy solution. Let's say we have two ordered lists of symbols (strings): ...
59 views

### Unique Identifier Creation and Invalidation

A colleague of mine recently interviewed for a software engineering job, and he was given a problem regarding unique identifier creation and testing for validation. So, the problem is: if a generated ...
507 views

### suffix tree: about Ukkonen's algorithm

I have specific question about suffix trees. I am reading the book Algorithms on strings_trees and sequence. I cannot understand details of Ukkonen's algorithm for constructing suffix trees. Why ...
513 views

### Is the running time of Boyer-Moore linear?

With pattern length $M$, text length $N$, and alphabet $\Sigma$, is the asymptotic running-time of Boyer-Moore $O(N/|\Sigma|)$ (even when $M$ grows larger than $|\Sigma|$)? Are there any sublinear ...