Related papers: Parallel Longest Common SubSequence Analysis In Ch…
Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines…
In this paper, we propose a data structure, a quadruple neighbor list (QN-list, for short), to support real time queries of all longest increasing subsequence (LIS) and LIS with constraints over sequential data streams. The QN-List built by…
Encoding long sequences in Natural Language Processing (NLP) is a challenging problem. Though recent pretraining language models achieve satisfying performances in many NLP tasks, they are still restricted by a pre-defined maximum length,…
Analyzing large-scale graphs poses challenges due to their increasing size and the demand for interactive and user-friendly analytics tools. These graphs arise from various domains, including cybersecurity, social sciences, health sciences,…
Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized…
The suffix array, perhaps the most important data structure in modern string processing, is often augmented with the longest common prefix (LCP) array which stores the lengths of the LCPs for lexicographically adjacent suffixes of a string.…
Sentence embedding models play a key role in various Natural Language Processing tasks, such as in Topic Modeling, Document Clustering and Recommendation Systems. However, these models rely heavily on parallel data, which can be scarce for…
Sequence-to-Sequence models were introduced to tackle many real-life problems like machine translation, summarization, image captioning, etc. The standard optimization algorithms are mainly based on example-to-example matching like maximum…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
Recently, Diffusion Large Language Models (DLLMs) have offered high throughput and effective sequential reasoning, making them a competitive alternative to autoregressive LLMs (ALLMs). However, parallel decoding, which enables simultaneous…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
We consider labeled directed graphs where each vertex is labeled with a non-empty string. Such labeled graphs are also known as non-linear texts in the literature. In this paper, we introduce a new problem of comparing two given labeled…
Average linkage Hierarchical Agglomerative Clustering (HAC) is an extensively studied and applied method for hierarchical clustering. Recent applications to massive datasets have driven significant interest in near-linear-time and efficient…
It has been proven that, when normalized by $n$, the expected length of a longest common subsequence of $d$ random strings of length $n$ over an alphabet of size $\sigma$ converges to some constant that depends only on $d$ and $\sigma$.…
Given two strings $A[1..n]$ and $B[1..m]$, and a set of operations allowed to edit the strings, the edit distance between $A$ and $B$ is the minimum number of operations required to transform $A$ into $B$. Sequentially, a standard Dynamic…
In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
Parallel sentence extraction is a task addressing the data sparsity problem found in multilingual natural language processing applications. We propose an end-to-end deep neural network approach to detect translational equivalence between…
The wide adoption of Large language models (LLMs) makes their dependability a pressing concern. Detection of errors is the first step to mitigating their impact on a system and thus, efficient error detection for LLMs is an important issue.…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…