Related papers: Does Preprocessing help in Fast Sequence Compariso…
In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
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…
Large volumes of text data have contributed significantly to the development of large language models (LLMs) in recent years. This data is typically acquired by scraping the internet, leading to pretraining datasets comprised of noisy web…
Distance computation is one of the most fundamental primitives used in communication networks. The cost of effectively and accurately computing pairwise network distances can become prohibitive in large-scale networks such as the Internet…
K-Means++ and its distributed variant K-Means$\|$ have become de facto tools for selecting the initial seeds of K-means. While alternatives have been developed, the effectiveness, ease of implementation, and theoretical grounding of the…
In this paper we give an algorithm for streaming $k$-edit approximate pattern matching which uses space $\widetilde{O}(k^2)$ and time $\widetilde{O}(k^2)$ per arriving symbol. This improves substantially on the recent algorithm of…
The edit distance $ed(X,Y)$ of two strings $X,Y\in \Sigma^*$ is the minimum number of character edits (insertions, deletions, and substitutions) needed to transform $X$ into $Y$. Its weighted counterpart $ed^w(X,Y)$ minimizes the total cost…
This paper aims at providing extremely efficient algorithms for approximate query enumeration on sparse databases, that come with performance and accuracy guarantees. We introduce a new model for approximate query enumeration on classes of…
The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence…
Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…
Deep neural networks have achieved impressive performance in many areas. Designing a fast and provable method for training neural networks is a fundamental question in machine learning. The classical training method requires paying…
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves…
In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…
We show that in the document exchange problem, where Alice holds $x \in \{0,1\}^n$ and Bob holds $y \in \{0,1\}^n$, Alice can send Bob a message of size $O(K(\log^2 K+\log n))$ bits such that Bob can recover $x$ using the message and his…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Text similarity calculation is a fundamental problem in natural language processing and related fields. In recent years, deep neural networks have been developed to perform the task and high performances have been achieved. The neural…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…