Related papers: $LCSk$++: Practical similarity metric for long str…

This paper addresses the Longest Filled Common Subsequence (LFCS) problem, a challenging NP-hard problem with applications in bioinformatics, including gene mutation prediction and genomic data reconstruction. Existing approaches, including…

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2,…

Given two equally long, uniformly random binary strings, the expected length of their longest common subsequence (LCS) is asymptotically proportional to the strings' length. Finding the proportionality coefficient $\gamma$, i.e. the limit…

The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…

Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array…

Code complexity metrics such as cyclomatic complexity have long been used to assess software quality and maintainability. With the rapid advancement of large language models (LLMs) on coding tasks, an important yet underexplored question…

Measuring similarities between strings is central for many established and fast growing research areas including information retrieval, biology, and natural language processing. The traditional approach for string similarity measurements is…

A new numerical characterization of symbolic sequences is proposed. The partition of sequence based on Ke and Tong algorithm is a starting point. Algorithm decomposes original sequence into set of distinct subsequences - a patterns. The set…

The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a…

Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…

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…

We provide a deterministic algorithm that outputs an $O(n^{3/4} \log n)$-approximation for the Longest Common Subsequence (LCS) of two input sequences of length $n$ in near-linear time. This is the first deterministic approximation…

This paper addresses the Restricted Longest Common Subsequence (RLCS) problem, an extension of the well-known Longest Common Subsequence (LCS) problem. This problem has significant applications in bioinformatics, particularly for…

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…

A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen…

Online string matching is a computational problem involving the search for patterns or substrings in a large text dataset, with the pattern and text being processed sequentially, without prior access to the entire text. Its relevance stems…

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…

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…

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 {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {\em longest common palindromic subsequence (LCPS)}…