Related papers: An Algorithm for the Longest Common Subsequence an…
The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…
In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…
In this paper we initiate the study of computing a maximal (not necessarily maximum) repeating pattern in a single input string, where the corresponding problems have been studied (e.g., a maximal common subsequence) only in two or more…
We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…
The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc.…
In the Palindrome Problem one tries to find all palindromes (palindromic substrings) in a given string. A palindrome is defined as a string which reads forwards the same as backwards, e.g., the string "racecar". A related problem is the…
Given a string $w$, another string $v$ is said to be a subsequence of $w$ if $v$ can be obtained from $w$ by removing some of its letters; on the other hand, $v$ is called an absent subsequence of $w$ if $v$ is not a subsequence of $w$. The…
We consider the problem of updating the information about multiple longest common sub-sequences. This kind of sub-sequences is used to highlight information that is shared across several information sequences, therefore it is extensively…
The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…
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…
Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…
Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation…
The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…
The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…
A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…
The expected length of longest common subsequences is a problem that has been in the literature for at least twenty five years. Determining the limiting constants \gamma_k appears to be quite difficult, and the current best bounds leave…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…
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…
The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE…