Efficiently Computing Minimal Absent Words and Extended Bispecial Factors with CDAWG Space

Core Concepts

The author presents a space-efficient data structure based on CDAWG to compute MAWs and EBFs, providing insights into bioinformatics and data compression applications.

Abstract

The content discusses the computation of minimal absent words (MAWs) and extended bispecial factors (EBFs) using a compact directed acyclic word graph (CDAWG). The focus is on non-trivial MAWs of length at least 2, with applications in bioinformatics and data compression. The proposed method offers efficient space utilization for outputting MAWs and EBFs in linear time relative to their sizes. Additionally, the relationship between MAWs, MRWs, MUSs, and EBFs is explored through the CDAWG structure. The authors introduce a more space-efficient data structure based on the compact DAWG (CDAWG) to compute MAWs in linear time with minimal space requirements. They demonstrate how MAWs are related to extended bispecial factors (EBFs) through the CDAWG representation. Furthermore, they discuss the connection between MRWs, MUSs, and EBFs within this computational framework. The study delves into combinatorial properties of MAWs, EBFs, and MRWs in strings represented by CDAWGs. Efficient algorithms are proposed for computing these structures with minimal space complexity while maintaining linear time performance relative to output size.

Stats

Fujishige et al. [16] proposed a data structure of size Θ(n) that can output the set MAW(S) of all MAWs for a given string S of length n in O(n+|MAW(S)|) time. The new data structure based on compact DAWG (CDAWG) can output MAW(S) in O(|MAW(S)|) time with O(emin) space. For any strings of length n, it holds that emin < 2n. There exists a family of strings S of length n such that er(S) = Θ(√n).

Quotes

"The proposed method offers efficient space utilization for outputting MAWs and EBFs in linear time relative to their sizes." "The study delves into combinatorial properties of MAWs, EBFs, and MRWs in strings represented by CDAWGs."

Key Insights Distilled From

Computing Minimal Absent Words and Extended Bispecial Factors with CDAWG Space

by Shunsuke Ine... at arxiv.org 02-29-2024

https://arxiv.org/pdf/2402.18090.pdf

Deeper Inquiries

How can the concept of minimal absent words be applied beyond bioinformatics

The concept of minimal absent words (MAWs) can be applied beyond bioinformatics in various fields such as data compression, natural language processing, and pattern recognition. In data compression, MAWs can be utilized to identify unique patterns or sequences that are absent in a dataset, leading to more efficient encoding schemes. In natural language processing, MAWs can help detect uncommon or rare words that do not appear frequently in a text corpus, aiding in tasks like sentiment analysis or authorship attribution. Additionally, in pattern recognition applications, MAWs can be used to find distinctive features or motifs that differentiate between different classes of data.

What potential challenges or limitations might arise when implementing CDAWG-based algorithms for real-world datasets

When implementing CDAWG-based algorithms for real-world datasets, several challenges and limitations may arise. One challenge is the scalability of the algorithm with large datasets. As the size of the input dataset increases, the space complexity of storing the compact directed acyclic word graph (CDAWG) may become prohibitive. Additionally, handling noisy or incomplete data could pose challenges as these algorithms rely on precise representations of strings and their relationships. Another limitation is related to computational efficiency when dealing with highly repetitive sequences. While CDAWGs offer space-efficient representations for repetitive strings by compacting identical substrings into shared nodes, navigating through these structures efficiently requires sophisticated algorithms and data structures. Moreover, ensuring robustness and accuracy when dealing with complex biological sequences or diverse textual data sets is crucial but challenging due to variations in sequence lengths and compositions across different domains.

How could advancements in computational biology benefit from exploring the relationships between different types of rare words

Advancements in computational biology could benefit significantly from exploring the relationships between different types of rare words such as minimal rare words (MRWs), minimal unique substrings (MUSs), extended bispecial factors (EBFs), and other similar concepts derived from string analysis techniques like CDAWGs. By understanding how these rare word types relate to each other within biological sequences such as DNA strands or protein sequences, researchers can gain insights into evolutionary processes, genetic mutations, functional regions within genomes/proteomes among species/varieties etc., which are vital for various biological studies including phylogenetics researches disease diagnostics drug development personalized medicine etc.