scholarly journals Properties of the extremal infinite smooth words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Srečko Brlek ◽  
Guy Melançon ◽  
Geneviève Paquin
Keyword(s):  
De Bruijn Graph ◽  
Lexicographical Order ◽  
Naive Algorithm ◽  
International Audience ◽  
De Bruijn

International audience Smooth words are connected to the Kolakoski sequence. We construct the maximal and the minimal in nite smooth words, with respect to the lexicographical order. The naive algorithm generating them is improved by using a reduction of the De Bruijn graph of their factors. We also study their Lyndon factorizations. Finally, we show that the minimal smooth word over the alphabet f1; 3g belongs to the orbit of the Fibonacci word.

scholarly journals Number of cycles in the graph of $312$-avoiding permutations

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Richard Ehrenborg ◽  
Sergey Kitaev ◽  
Einar Steingrımsson
Keyword(s):  
Nous Avons ◽  
De Bruijn Graph ◽  
International Audience ◽  
De Bruijn ◽  
Affine Permutations ◽  
Number Of Cycles

International audience The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping $312$-avoiding permutations. Using this we also give a refinement of the enumeration of $312$-avoiding affine permutations. Le graphique de permutations qui se chevauchent est définie d’une manière analogue à celle du graphe de De Bruijn sur des chaînes de symboles. Cependant, au lieu d’exiger la queue d’une permutation d’égaler la tête d’un autre pour qu’ils soient reliés par un bord, nous avons besoin que la tête et la queue en question ont leurs lettres apparaissent dans le même ordre de grandeur. Nous donnons une formule pour le nombre de cycles de longueur$d$ dans le sous- graphe de chevauchement $312$-évitant permutations. L’utilisation de ce nous donnent également un raffinement de l’énumération de$312$-évitant permutations affines.

scholarly journals Fast and efficient Rmap assembly using the Bi-labelled de Bruijn graph

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Kingshuk Mukherjee ◽  
Massimiliano Rossi ◽  
Leena Salmela ◽  
Christina Boucher
Keyword(s):  
Single Molecule ◽  
De Bruijn Graph ◽  
Anabas Testudineus ◽  
E Coli ◽  
Genome Wide ◽  
A Genome ◽  
De Bruijn ◽  
Optical Maps ◽  
Definition Of ◽  
Numeric Representation

AbstractGenome wide optical maps are high resolution restriction maps that give a unique numeric representation to a genome. They are produced by assembling hundreds of thousands of single molecule optical maps, which are called Rmaps. Unfortunately, there are very few choices for assembling Rmap data. There exists only one publicly-available non-proprietary method for assembly and one proprietary software that is available via an executable. Furthermore, the publicly-available method, by Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006), follows the overlap-layout-consensus (OLC) paradigm, and therefore, is unable to scale for relatively large genomes. The algorithm behind the proprietary method, Bionano Genomics’ Solve, is largely unknown. In this paper, we extend the definition of bi-labels in the paired de Bruijn graph to the context of optical mapping data, and present the first de Bruijn graph based method for Rmap assembly. We implement our approach, which we refer to as rmapper, and compare its performance against the assembler of Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006) and Solve by Bionano Genomics on data from three genomes: E. coli, human, and climbing perch fish (Anabas Testudineus). Our method was able to successfully run on all three genomes. The method of Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006) only successfully ran on E. coli. Moreover, on the human genome rmapper was at least 130 times faster than Bionano Solve, used five times less memory and produced the highest genome fraction with zero mis-assemblies. Our software, rmapper is written in C++ and is publicly available under GNU General Public License at https://github.com/kingufl/Rmapper.

A novel 3D NoC architecture based on De Bruijn graph

2012 ◽  
Vol 38 (3) ◽  
pp. 801-810 ◽  
Author(s):  
Yiou Chen ◽  
Jianhao Hu ◽  
Xiang Ling ◽  
Tingting Huang
Keyword(s):  
De Bruijn Graph ◽  
De Bruijn

scholarly journals SOME EXPERIMENTS ON THE CONSTRUCTION AND ANALYSIS OF THE DE BRUIJN GRAPH

2020 ◽  
Author(s):  
Alexander G. Marchuk ◽  
◽  
Sergey Nikolaevich Troshkov ◽  
Keyword(s):  
Data Storage ◽  
Parallel Computations ◽  
De Bruijn Graph ◽  
Distributed Data ◽  
Distributed Data Storage ◽  
De Bruijn

This paper describes the experience of solving the problem of finding chains in the De Bruijn graph using parallel computations and distributed data storage.

On the connectivity of the De Bruijn graph

1988 ◽  
Vol 27 (6) ◽  
pp. 315-318 ◽  
Author(s):  
M.A. Sridhar
Keyword(s):  
De Bruijn Graph ◽  
De Bruijn
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