Related papers: A Note on the Longest Common Compatible Prefix Pro…

The Longest Common Subsequence (LCS) problem is a fundamental problem of sequence comparison. A natural approximation to this problem is a model in which every pairs of letters of two ``sequences'' are matched independently of the other…

This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…

When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main…

Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…

We consider approximate circular pattern matching (CPM, in short) under the Hamming and edit distance, in which we are given a length-$n$ text $T$, a length-$m$ pattern $P$, and a threshold $k>0$, and we are to report all starting positions…

We give a sublinear quantum algorithm for the longest common substring (LCS) problem on the run-length encoded (RLE) inputs, under the assumption that the prefix-sums of the runs are given. Our algorithm costs $\tilde{O}(n^{5/6})\cdot…

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

Lyndon words have been largely investigated and showned to be a useful tool to prove interesting combinatorial properties of words. In this paper we state new properties of both Lyndon and inverse Lyndon factorizations of a word $w$, with…

The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an $O(n^2)$-time algorithm and a SETH-based conditional lower…

The dictionary matching with gaps problem is to preprocess a dictionary $D$ of $d$ gapped patterns $P_1,\ldots,P_d$ over alphabet $\Sigma$, where each gapped pattern $P_i$ is a sequence of subpatterns separated by bounded sequences of don't…

Suffix arrays encode the lexicographical order of all suffixes of a text and are often combined with the Longest Common Prefix array (LCP) to simulate navigational queries on the suffix tree in reduced space. In space-critical applications…

Let $w$ be a string of length $n$. The problem of counting factors crossing a position - Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Leqroc, and Rytter, 2021], asks to count the number $\mathcal{C}(w,k)$…

Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $\delta$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequence for both $A$ and $B$ such that for…

The all-pairs suffix-prefix (APSP) problem is a classical problem in string processing which has important applications in bioinformatics. Given a set $\mathcal{S} = \{S_1, \ldots, S_k\}$ of $k$ strings, the APSP problem asks one to compute…

The longest common subsequence (LCS) is a fundamental problem in string processing which has numerous algorithmic studies, extensions, and applications. A sequence $u_1, \ldots, u_f$ of $f$ strings s said to be an ($f$-)segmentation of a…

In this paper, we attempt to solve the problem of Prepositional Phrase (PP) attachments in English. The motivation for the work comes from NLP applications like Machine Translation, for which, getting the correct attachment of prepositions…

We generalise a multiple string pattern matching algorithm, recently proposed by Fredriksson and Grabowski [J. Discr. Alg. 7, 2009], to deal with arbitrary dictionaries on an alphabet of size $s$. If $r_m$ is the number of words of length…

Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…

In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for…

Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…