Related papers: Approximating LCS and Alignment Distance over Mult…
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…
Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS)…
Real-world data often comes in compressed form. Analyzing compressed data directly (without decompressing it) can save space and time by orders of magnitude. In this work, we focus on fundamental sequence comparison problems and try to…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
We study sublinear time algorithms for estimating the size of maximum matching. After a long line of research, the problem was finally settled by Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation factor of $2$.…
Multiple Sequences Alignment (MSA) of biological sequences is a fundamental problem in computational biology due to its critical significance in wide ranging applications including haplotype reconstruction, sequence homology, phylogenetic…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
Multiple sequence alignment is a basic procedure in molecular biology, and it is often treated as being essentially a solved computational problem. However, this is not so, and here I review the evidence for this claim, and outline the…
One of the most fundamental method for comparing two given strings $A$ and $B$ is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of $A$ and $B$. In this paper, we deal with the STR-IC-LCS problem…
The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…
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…
Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…
We propose a metric for the space of multiple sequence alignments that can be used to compare two alignments to each other. In the case where one of the alignments is a reference alignment, the resulting accuracy measure improves upon…
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…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length…
Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$…
In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…
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…