Questions tagged [strings]

Questions about sequences of symbols, sets thereof and their properties as well as uses.

115 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
23
votes
1answer
1k views

Compression of domain names

I am curious as to how one might very compactly compress the domain of an arbitrary IDN hostname (as defined by RFC5890) and suspect this could become an interesting challenge. A Unicode host or ...
10
votes
1answer
4k views

Finding the longest repeating subsequence

Given a string $s$, I would like to find the longest repeating (at least twice) subsequence. That is, I would like to find a string $w$ which is a subsequence (doesn't have to be a contiguous) of $s$ ...
8
votes
2answers
1k views

Count of distinct substrings in string inside range

Having string $S$ of length $n$, finding the count of distinct substrings can be done in linear time using LCP array. Instead of asking for unique substrings count in whole string $S$, query $q$ ...
7
votes
0answers
861 views

Minimal regular expression that matches a given set of words

I have a dictionary-like regular expression, an "or chain" of words, word1|word2|word3|... Unfortunately, the chain is too large. I'd like to find the minimal ...
6
votes
0answers
147 views

Counting number of swaps to make two strings equal in linear time

The input to our problem is a pair of strings, say $x$ and $y$. We treat our alphabet size as a constant, i.e., our input is effectively a pair of arrays with the values therein bounded by a constant. ...
6
votes
1answer
130 views

Find the 'best' longest common subsequence

I am writing a program that computes and displays diffs. I implemented Meyers algorithm that computes the LCS between 2 subsequences (seq1 and ...
6
votes
0answers
105 views

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 $\...
6
votes
0answers
80 views

What is longest string with no equidistant pairs of equal characters for a given alphabet?

Given a finite alphabet $A$ with $|A|=n$, what is the largest $l$ so that a string $s=a_1...a_l$ of length $l$ exists with $a_i\in A$ so that there is no $i,j,d$ with $i\neq j, d > 0$ so that $a_i =...
5
votes
0answers
53 views

Highest covering repeated string

Let's say I have the following string: XXXXXAYYYYBYYYYCXXXXXDYYYY We can see that the substring XXXXX is 5 characters long, ...
5
votes
0answers
125 views

Partitioning through block moves to the end

Suppose we have a binary string $s$. We wish to partition this string in a series of $0$s followed by $1$s (alternatively: we wish to sort), using only one operation: moving three consecutive elements ...
5
votes
0answers
165 views

Count Wildcard Parenthesizations of a String

Let $\Sigma = \{ (, ), ? \}$ be an alphabet. For a given string $s \in \Sigma^*$, we denote by $f(s)$ the number of ways to replace each symbol $?$ either with $($ or with $)$ such that $s$ is ...
5
votes
0answers
393 views

Number of distinct substrings

I know how to find the number of distinct substrings for a string (using suffix arrays) and I was wondering if there was a way to find this number for all of its prefixes. I already have an $O(N^2)$ ...
4
votes
1answer
72 views

Evaluating predicate on binary strings

Consider two unknown binary strings $$X = x_{1} x_{2} \dots x_{n^{2}}, \quad Y = y_{1} y_{2} \dots y_{n^{2}}, \quad x_{i}, y_{i} \in \{0, 1\} .$$ We may request a string $Z = z_{1} z_{2} \dots z_{n^{2}...
4
votes
0answers
403 views

KMP Algorithm, Pratt's Minimisation/optimization of Knuth's original DFA based algorithm

The Original Knuth's Algorithm is based on DFA and it depends on the alphabet size. And Then, Pratt optimised it to be independent of Alphabet Size. But, All the ...
4
votes
0answers
590 views

Distinguishing probabilistic, deterministic, and fuzzy matching methods

I have two datasets that I am trying to match to one another. One dataset's contents is a subset of the other, but contains typographical errors of varying types and magnitude. I am applying the ...
3
votes
0answers
80 views

Remove a subsequence from a string and append it at the end

Consider the following operation on strings: pick a (not necessarily contiguous) subsequence, remove it and then append all the characters in the same order at the end. This operation preserves the ...
3
votes
0answers
40 views

Why does it take more than the original alphabet to generate sets of strings?

I am reading Computability by Nigel Cutland and I'm stumped on a brief statement about generating particular sets of strings that is not explained or given any examples. First, here are some ...
3
votes
0answers
32 views

String to small integer mapping without collision

Is there any good approach to devise a mapping of limited number of strings $N_1 << 2^{15}$ to integers less than $2^{15}$ without conflicts? Strings are quite often of the form of prefix + ...
3
votes
0answers
662 views

Finding multi word anagrams from a set of words

Finding all anagrams for a word $w$ from a set of words is a problem with many well-known solutions (for example make a hash table mapping from the bag of letters of a word to the word). But what ...
3
votes
0answers
144 views

String version of even-odd partition problem

Motivated by Hardness proof of EVEN-ODD PARTITION post I came up with a string version. String even-odd partition INPUT: $(x_{1,0},x_{1,1}),\dots,(x_{n,0},x_{n,1})$, i.e., $n$ pairs of strings over ...
3
votes
0answers
80 views

What is the intuition behind the "edit sensitive parsing" tree?

If I understand right then ESP tree is defined as : given any string $x$ of finite length over an alphabet one can construct "an" ESP tree corresponding to it say $T_x$ such that each leaf of the tree ...
3
votes
0answers
710 views

Myers' Fast bit-vector algorithm in plain English?

Inspired by this question on Suffix Trees, and the fabulous winning answer, I would hereby ask for a similar explanation of Myers' Fast Bit-Vector Algorithm for Approximate String Matching Based on ...
2
votes
0answers
220 views

Should a prefix tree (trie) node store only a single character or a string?

I've just implemented a Trie and I thought it would be a good idea to store strings in the Trie nodes in contrast to storing single characters. Storing strings is for sure more space-efficient and ...
2
votes
0answers
144 views

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 ...
2
votes
0answers
37 views

Permutation to maximise strings' common prefix

Is there a good algorithm for finding a permutation which, applied to all the strings in a set, maximises the weight of those with a common fixed length prefix. Given a set $S=\{(s,w)\}$ of pairs of ...
2
votes
1answer
4k views

Convert given string to Palindrome with given substring

Given a String S1 and String S2. Convert string S1 to a palindrome string such S2 is a substring of that palindromic string. Only operation allowed on S1 is replacement of any character with any other ...
2
votes
0answers
73 views

Minimization of simple cyclic automata

Version 1 of the question: I am looking for any correct $O(n)$ algorithm in the literature which will solve the DFA minimization problem referred to in the quote below from [Almeida & Zeitoun 2008]...
2
votes
0answers
55 views

Bad character rule in the Apostolico–Giancarlo algorithm

In the paper "Tight bounds on the complexity of the Apostoliko-Giancarlo algorithm" by Crochemore and Lecroq authors prove that algorithm performs not more than $1.5n$ comparison of characters in the ...
2
votes
0answers
58 views

Forward error correction for for long strings of bits

Let $a$ be a large string of bits that is transmitted over a channel that introduces errors (insertions, deletions or substitutions) where the probability of an error happening is $p=0.01$ for each ...
2
votes
0answers
200 views

Calculating Contiguous String Kernel efficiently

I am given two strings, $\overline{a},\overline{b}$ in a finite alphabet, $\Sigma$, and a positive integer $k$. I want to compute the $k$-th order contiguous string kernel, which is defined to be ...
2
votes
0answers
75 views

Correct bracketing check with rotate operation on position i

Given sequence (length $N$) of brackets like $($ and $)$. The task is to implement data structure which supports following operations: Check whether the sequence is correctly bracketed Rotate bracket ...
2
votes
0answers
343 views

Fast generalised suffix array construction: lower than O(n^2 log n)

There is a lot in the literature about linear time constructions for suffix arrays; DC3, radixSA46, and more... However, these, I believe, are only for suffix arrays; with a single string input. Are ...
2
votes
0answers
986 views

Using Jaro-Winkler similarity to recognize matching strings

How do I use the Jaro-Winkler similarity measure to test whether two strings should be considered to match each other? I tried comparing the Jaro-Winkler score to a fixed threshold: e.g., if the ...
2
votes
0answers
689 views

Efficient algorithm to approximate membership in a set of strings

I devised an algorithm / data structure and I would like to ask whether it already exists. The problem statement is: after having added some number of strings to the set, determine whether a given ...
2
votes
0answers
555 views

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 ...
2
votes
0answers
287 views

palindromic factorization

Is there a linear time algorithm that, given a string of length n, tells if it is a sequence of non overlapping palindromes (each of even length, in a binary alphabet)?? I found algorithms that return ...
2
votes
0answers
98 views

How does a minimal DFA ensure minimal computational cost?

I just went to read wikipedia to check a point on FA minimization, and I read there the following sentence: The minimal DFA ensures minimal computational cost for tasks such as pattern matching. ...
2
votes
0answers
104 views

What is hiding behind amortized constant delay enumeration?

The following may contain errors. It is precisely because I am not sure I understand the topic that I am asking questions. I do not have books about it and could not find an adequate reference on the ...
1
vote
0answers
29 views

Longest substring creating palindromic substring in other string

Given two strings $s, t$, I would liketo find a maximal subsequence of $t$ (denoted as $t'$), such that the concatenation of $t'$ with its reverse ($t'_R$), is a palindromic substring of $s$. I ...
1
vote
0answers
48 views

Longest palindrome after swapping operation

I know that Manacher's algorithm can be used to find the longest palindromic substring of a string in linear time. But I want to find the longest palindromic substring after swapping any two indices ...
1
vote
1answer
208 views

calculating the string similarity of an optimal alignment

description of the algorithms behavior I have two strings s1 and s2, with $len\_s1 <= len\_s2$. I would like to find the ...
1
vote
0answers
114 views

Boyer-Moore jump table

I have a pattern $P$ of length $m$, i.e. $P = p_0, p_1, \ldots, p_{m-1}$ which I want to build a simple jump table for (not considering special optimizing cases for now). I only want to build a jump ...
1
vote
0answers
57 views

Number of words of length n for special language

Let $\Sigma$ be an alphabet and let $L$ be a language over it with the following properties: if $w\in L$ then there exists $v\in \Sigma^*$ such that $wv \in L$ and for every $s\in \Sigma$ the word $...
1
vote
0answers
31 views

What is the appropriate term for the "string splitting" problem?

To be clear, I didn't hear of this in any particular venue, and so can't point you to one. Two variants that I can bring you: String spitting Given a string (sequence of elements), and a function ...
1
vote
1answer
134 views

finding all cyclic substrings of a string

I have been stuck on this problem for a while now; any help would be appreciated. Given a string S, find the number of distinct substrings which are composed of 2 or more consecutive strings. For ...
1
vote
0answers
98 views

Fastest way to find a substring 'ab' inside a string 'abab'

Let $A$ be an input alphabet - a finite set of symbols. Elements of $A$ are called the characters. The alphabet I am interested in is the set of all ordinary letters ...
1
vote
0answers
15 views

Finding fewest strings that cover $\Sigma^n$ up to $R$ edit operations

Let $\Sigma$ be the alphabet, $0<R<n$ be an integer and let $\Sigma^n$ denote the set of all strings of length $n$ over the alphabet. The task is to find the minimum $m$ such that there exist ...
1
vote
0answers
97 views

Finding bounded lexicographically largest string of digits but not larger than other with counted substitutions

The problem comes from the book текстовые и жадные алгоритмы (String and greedy algorithms) by a fairly unknown Russian computer scientist Николай Сухоруков. We are given two numbers $A$ and $B$ of ...
1
vote
0answers
26 views

Algorithm for searching string with wildcards

I'm trying to find efficient algorithm for checking if string with wildcards contains given substring. The parts of the string are separated with a "." character. So for example I have ...
1
vote
0answers
96 views

Is there a less than $O(n)$ algorithm for converting UTF-8 character offsets to byte offsets, in a gap buffer?

A Gap Buffer is a variation on a dynamically-sized array, but with a gap inside it. The gap makes editing operations around the gap more efficient. Deletion before the gap can be implemented by simply ...