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Questions tagged [string-matching]

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2
votes
1answer
63 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 ...
10
votes
2answers
267 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 ...
1
vote
1answer
248 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 ...
10
votes
1answer
300 views

Pattern matching with don't cares: multiple patterns

Kalai's 2-page SODA paper gives a simple and efficient algorithm for pattern matching with don't cares (wildcards that match one character). In essence, it is as easy as convolution. But what happens ...
5
votes
0answers
78 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 $H(s) = h(s_1)h(s_2)\dots h(s_n)$ ...
2
votes
0answers
130 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.
12
votes
1answer
354 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 ...
11
votes
1answer
962 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 ...
0
votes
1answer
76 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 ...
2
votes
1answer
132 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 ...
4
votes
1answer
568 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)...
0
votes
1answer
420 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 ...
0
votes
0answers
277 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): ...
3
votes
2answers
152 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 ...
26
votes
1answer
627 views

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 ...
1
vote
1answer
432 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." ...
0
votes
1answer
58 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 ...
2
votes
3answers
292 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 ...
8
votes
0answers
191 views

Simplifying the disjoint union of wildcard strings

Setting: patterns with "don't care" symbols, binary alphabet. For example, pattern $x = 001?$ represents the set $L(x) = \{0010, 0011\}$. We are given a set $P$ of disjoint patterns: $L(x) \cap L(y) ...
13
votes
2answers
774 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 ...
10
votes
4answers
5k views

Can Suffix trees be used to find all common substrings?

I am trying to use suffix trees to compare string sequences. I have found implementations/theory for the longest common sub string problem using suffix trees. However, What i am looking for is a ...
0
votes
0answers
492 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 ...
1
vote
2answers
292 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. ...
20
votes
2answers
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 ...
0
votes
1answer
816 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.
-4
votes
3answers
125 views

Text Analyze and Processing

What algorithms do you know regarding text analyze/processing? Detailed, I need to "find out" the most used words, sentences, words' combinations, their category etc (these are just examples, moreover ...
10
votes
3answers
712 views

Permutation pattern matching in strings

Loosely speaking, permutation pattern matching deals with problems of the following kind: Given permutations $\pi$ in $S_n$ and $\sigma$ in $S_m$, with $m\leq n$, does $\pi$ contain a subsequence $...
6
votes
1answer
275 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 ...
9
votes
1answer
551 views

Deciding if a wildcard string is completely matched by another wildcard string in a set

Here's a problem that has been bugging me for a while. Let's say a string is a sequence of 1s and 0s, and a wildcard string is a sequence of 1, 0, and ?s. All strings and wildcard strings have the ...
5
votes
2answers
329 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 ...
24
votes
8answers
4k 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, ...
3
votes
1answer
332 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 ...
-1
votes
1answer
378 views

Locate “N Gram” substrings that are smallest distance away from a target string N character long

I am looking for an algorithm, or code, preferably in Python that would help me locate substrings, N characters long, of exisiting strings that are closest to a target string N character long. ...
8
votes
4answers
721 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 ...