Related papers: Mean-Field Approximations to the Longest Common Su…
Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…
Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…
Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence. If $\ell$ is the length of the overlap, we prove that the expected…
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…
In the longest common substring problem, we are given two strings of length $n$ and must find a substring of maximal length that occurs in both strings. It is well known that the problem can be solved in linear time, but the solution is not…
In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to…
The problem of finding a longest common subsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence…
The graph retrieval problem is to search in a large corpus of graphs for ones that are most similar to a query graph. A common consideration for scoring similarity is the maximum common subgraph (MCS) between the query and corpus graphs,…
Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is…
The Average Common Substring (ACS) is a popular alignment-free distance measure for phylogeny reconstruction. The ACS can be computed in O(n) space and time, where n=x+y is the input size. The compressed string matching is the study of…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
A technique using a systolic array structure is proposed for solving the common approximate substring (CAS) problem. This approach extends the technique introduced in earlier work from the computation of the edit-distance between two…
We study the problem of computing a longest increasing subsequence in a sequence $S$ of $n$ distinct elements in the presence of persistent comparison errors. In this model, every comparison between two elements can return the wrong result…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
The problem of the fluctuation of the Longest Common Subsequence (LCS) of two i.i.d. sequences of length $n>0$ has been open for decades. There exist contradicting conjectures on the topic. Chvatal and Sankoff conjectured in 1975 that…
We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n,…
A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…