scholarly journals On the longest common prefix of suffixes in an inverse Lyndon factorization and other properties

Author(s):  
Paola Bonizzoni ◽  
Clelia De Felice ◽  
Rocco Zaccagnino ◽  
Rosalba Zizza
Keyword(s):  
2019 ◽  
Vol 12 (2) ◽  
pp. 128-134
Author(s):  
Sanjeev Kumar ◽  
Suneeta Agarwal ◽  
Ranvijay

Background: DNA and Protein sequences of an organism contain a variety of repeated structures of various types. These repeated structures play an important role in Molecular biology as they are related to genetic backgrounds of inherited diseases. They also serve as a marker for DNA mapping and DNA fingerprinting. Efficient searching of maximal and super maximal repeats in DNA/Protein sequences can lead to many other applications in the area of genomics. Moreover, these repeats can also be used for identification of critical diseases by finding the similarity between frequency distributions of repeats in viruses and genomes (without using alignment algorithms). Objective: The study aims to develop an efficient tool for searching maximal and super maximal repeats in large DNA/Protein sequences. Methods: The proposed tool uses a newly introduced data structure Induced Enhanced Suffix Array (IESA). IESA is an extension of enhanced suffix array. It uses induced suffix array instead of classical suffix array. IESA consists of Induced Suffix Array (ISA) and an additional array-Longest Common Prefix (LCP) array. ISA is an array of all sorted suffixes of the input sequence while LCP array stores the lengths of the longest common prefixes between all pairs of consecutive suffixes in an induced suffix array. IESA is known to be efficient w.r.t. both time and space. It facilitates the use of secondary memory for constructing the large suffix-array. Results: An open source standalone tool named MSR-IESA for searching maximal and super maximal repeats in DNA/Protein sequences is provided at https://github.com/sanjeevalg/MSRIESA. Experimental results show that the proposed algorithm outperforms other state of the art works w.r.t. to both time and space. Conclusion: The proposed tool MSR-IESA is remarkably efficient for the analysis of DNA/Protein sequences, having maximal and super maximal repeats of any length. It can be used for identification of well-known diseases.


2018 ◽  
Author(s):  
Felipe A. Louza ◽  
Guilherme P. Telles ◽  
Simon Gog

Strings are prevalent in Computer Science and algorithms for their efficient processing are fundamental in various applications. The results introduced in this work contribute with theoretical improvements and practical advances in building full-text indexes. Our first contribution is an in-place algorithm that computes the Burrows-Wheeler transform and the longest common prefix (LCP) array. Our second contribution is the construction of the suffix array augmented with the LCP array in optimal time and space for strings from constant size alphabets. Our third contribution is a set of algorithms to construct full-text indexes for string collections in optimal theoretical bounds. This work is an extended abstract of the Ph.D. thesis of the first author.


Author(s):  
Juha Kärkkäinen ◽  
Giovanni Manzini ◽  
Simon J. Puglisi

2021 ◽  
pp. 143-150
Author(s):  
Tomohiro I ◽  
Robert W. Irving ◽  
Dominik Köppl ◽  
Lorna Love

2014 ◽  
Vol 15 (1) ◽  
pp. 187 ◽  
Author(s):  
Alex Rudniy ◽  
Min Song ◽  
James Geller

2019 ◽  
Vol 30 (08) ◽  
pp. 1363-1379
Author(s):  
Lucas Mol ◽  
Narad Rampersad ◽  
Jeffrey Shallit ◽  
Manon Stipulanti

We make certain bounds in Krebs’ proof of Cobham’s theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic [Formula: see text]-automatic sequence and an aperiodic [Formula: see text]-automatic sequence, where [Formula: see text] and [Formula: see text] are multiplicatively independent. We also show that an automatic sequence cannot have arbitrarily large factors in common with a Sturmian sequence.


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