Related papers: On the String Consensus Problem and the Manhattan …

The NP-hard Minimum Common String Partition problem asks whether two strings $x$ and $y$ can each be partitioned into at most $k$ substrings, called blocks, such that both partitions use exactly the same blocks in a different order. We…

Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover,…

Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we…

Large language models (LLMs) frequently generate multiple candidate responses for a given prompt, yet selecting the most reliable one remains challenging, especially when correctness diverges from surface-level majority agreement. Existing…

The Universal Similarity Metric (USM) has been demonstrated to give practically useful measures of "similarity" between sequence data. Here we have used the USM as an alternative distance metric in a K-Nearest Neighbours (K-NN) learner to…

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.…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…

Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…

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 $k$-center problem is a fundamental optimization problem with numerous applications in machine learning, data analysis, data mining, and communication networks. The $k$-center problem has been extensively studied in the classical…

In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…

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…

In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings $S$ and $T$ of lengths $n$ and $m$, respectively, to obtain a data-structure that is able to answer…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…