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Construction of de Bruijn sequences of minimal complexity

T. Etzion, A. Lempel
1984 IEEE Transactions on Information Theory  
It is well known that the linear complexity of a de Bruijn sequence S of length 2" is bounded below by 2"-' + n for n > 3. It is shown that this lower bound is attainable for all n. THEORY, VOL.  ...  A SUFFICIENT CONDITION FOR THE EXISTENCE OF DE BRUIJN SEQUENCES OF MINIMAL COMPLEXITY In this section we derive a sufficient condition for the existence of de Bruijn sequences of order n with minimal complexity  ...  We investigate the linear-complexity distribution of binary de Bruijn sequences of given length.  ... 
doi:10.1109/tit.1984.1056965 fatcat:s4vvhdoa4rfzhgs3plxxmpwi3m

On the distribution of de bruijn sequences of low complexity

Tuvi Etzion
1985 Journal of combinatorial theory. Series A  
First, we give examples of de Bruijn sequences of minimal complexity for n = 7 and n = 8.  ...  Conjecture A is valid for 3 Q n < 5, and for all the de Bruijn sequences of minimal complexity which we check for n = 6.  ... 
doi:10.1016/0097-3165(85)90074-3 fatcat:t3ggqqu2sfa5lfu6xhsafonnzi

On the Minimum Linear Complexity of de Bruijn Sequences over Non-prime Finite Fields

Peter A. Hines
1999 Journal of combinatorial theory. Series A  
It has been conjectured that over any non-prime finite field F p m and for any positive integer n, there exists a span n de Bruijn sequence over F p m which has the minimum possible linear complexity p  ...  We give a proof by construction that this conjecture is true.  ...  To construct a span n de Bruijn sequence over F p m of minimal linear complexity, we begin by taking an arbitrary span n de Bruijn sequence s over F p m&1 and``extend'' it into a span n de Bruijn sequence  ... 
doi:10.1006/jcta.1998.2920 fatcat:vw6tvc6spba23pb5vixaxyvwbu

Cryptographically Strong de Bruijn Sequences with Large Periods [chapter]

Kalikinkar Mandal, Guang Gong
2013 Lecture Notes in Computer Science  
s technique for producing de Bruijn sequences through compositions. We then conduct an analysis on an approximation of the feedback functions that generate de Bruijn sequences.  ...  Furthermore, we present a compact algebraic representation of an (n + 16)-stage nonlinear feedback shift register (NLFSR) and a few examples of de Bruijn sequences of period 2 n , 35 ≤ n ≤ 40, which are  ...  By this technique, one can generate a de Bruijn sequence from an m-sequence. The linear complexity of this type of de Bruijn sequences is at least 2 n−1 + n + 1 [2] .  ... 
doi:10.1007/978-3-642-35999-6_8 fatcat:2xvvxnx4rne4vknaztoa5h36ia

Minimal Eulerian trail in a labeled digraph [article]

Martin Matamala, Eduardo Moreno
2005 arXiv   pre-print
We also show an application of this algorithm to construct the minimal de Bruijn sequence of a language.  ...  In this work, we present an algorithm to construct the Eulerian trail starting at an arbitrary vertex v of minimum lexicographical label among labels of all Eulerian trails starting at this vertex.  ...  Finally, in Section 3 we give an application of this algorithm to construct the minimal de Bruijn sequence of a language.  ... 
arXiv:cs/0505036v1 fatcat:wg3yrrcqmneg3dn46oq7owa26i

Permutation Polynomials, de Bruijn Sequences, and Linear Complexity

Simon R. Blackburn, Tuvi Etzion, Kenneth G. Paterson
1996 Journal of combinatorial theory. Series A  
The connection is used both to construct span 1 de Bruijn sequences (permutations) of a range of linear complexities and to prove non-existence results for arbitrary spans.  ...  Upper and lower bounds for the linear complexity of a de Bruijn sequence of span n over a finite field are established.  ...  That this is the case is a simple consequence of the construction of v from T and A. K A Construction for de Bruijn Sequences of Minimal Complexity Construction 27.  ... 
doi:10.1006/jcta.1996.0088 fatcat:quu2lgo2ivdsbeytymsnikowgi

Minimal Eulerian Circuit in a Labeled Digraph [chapter]

Eduardo Moreno, Martín Matamala
2006 Lecture Notes in Computer Science  
We also show an application of this algorithm to construct the minimal De Bruijn sequence of a language.  ...  We present an algorithm to construct the unique Eulerian circuit of lexicographically minimal label starting at a fixed vertex.  ...  Finally, in Section 4 we show an application of this algorithm to construct the minimal De Bruijn sequence of a language.  ... 
doi:10.1007/11682462_67 fatcat:ofrxbv7srjckdiyixs337ef46m

De Bruijn sequences with efficient decoding algorithms

Jonathan Tuliani
2001 Discrete Mathematics  
A de Bruijn sequence of span n is a periodic sequence in which every n-tuple over the alphabet appears exactly once, starting within the minimal generating cycle of the sequence.  ...  These results include a construction for binary de Bruijn sequences of arbitrary span whose decoding algorithm is both fast and storage-free.  ...  The complexity follows from Lemma 22. span n de Bruijn sequence [s] using Construction 2.  ... 
doi:10.1016/s0012-365x(00)00117-5 fatcat:kau7udrrgnaqxjr3quribfpney

Indexing De Bruijn graphs with minimizers [article]

Camille Marchet, Mael Kerbiriou, Antoine Limasset
2019 biorxiv/medrxiv   pre-print
Moreover, it can be efficiently built from the De Bruijn graph sequences.  ...  To leverage this challenge, recent works take advantage of the k-mer sets properties. They exploit the overlaps shared among k-mers by using a De Bruijn graph as a compact k-mer set.  ...  This work was supported by the ANR Transipedia (ANR-18-CE45-0020), and benefited from Université de Lille HPC Cloud computing resources.  ... 
doi:10.1101/546309 fatcat:szs2yd455bfptmwumelz5yiaka

Space-efficient and exact de Bruijn graph representation based on a Bloom filter

Rayan Chikhi, Guillaume Rizk
2013 Algorithms for Molecular Biology  
The de Bruijn graph data structure is widely used in next-generation sequencing (NGS). Many programs, e.g. de novo assemblers, rely on in-memory representation of this graph.  ...  However, current techniques for representing the de Bruijn graph of a human genome require a large amount of memory (≥ 30 GB).  ...  Background The de Bruijn graph of a set of DNA or RNA sequences is a data structure which plays an increasingly important role in next-generation sequencing applications.  ... 
doi:10.1186/1748-7188-8-22 pmid:24040893 pmcid:PMC3848682 fatcat:6ltoll4ztrgh3nwjxtntsezwym

Bifrost – Highly parallel construction and indexing of colored and compacted de Bruijn graphs [article]

Guillaume Holley, Páll Melsted
2019 bioRxiv   pre-print
Results: We present a new parallel and memory efficient algorithm enabling the direct construction of the compacted de Bruijn graph without producing the intermediate uncompacted de Bruijn graph.  ...  For population genomic analysis, the colored de Bruijn graph is often used in order to take advantage of the massive sets of sequenced genomes available for each species.  ...  draft of the software.  ... 
doi:10.1101/695338 fatcat:a7wnmn7ovnav3h6tw6sysrbkby

Graph theoretical Strategies in De Novo Assembling

Kimia Behizadi, Nafiseh Jafarzadeh, Ali Iranmanesh
2022 IEEE Access  
INDEX TERMS Combinatorial data structures, de-Bruijn graph, de novo assembly algorithms, high throughput sequencing, overlap graph.  ...  Algorithms for de novo assembly have been developed to deal with and assemble a large number of short sequence reads from genome sequencing.  ...  The most commonly used approach to construct a de-Bruijn graph for genome assembly is the Eulerian DBG which has polynomial time complexity. 1) DE-BRUIJN GRAPH-BASED ASSEMBLERS Assembler EULER [11]  ... 
doi:10.1109/access.2022.3144113 fatcat:iajrk3fq6jhbfel7apoowu3v2m

Bifrost: highly parallel construction and indexing of colored and compacted de Bruijn graphs

Guillaume Holley, Páll Melsted
2020 Genome Biology  
Memory consumption of de Bruijn graphs is often prohibitive.  ...  We present a parallel and memory-efficient algorithm enabling the direct construction of the compacted de Bruijn graph without producing the intermediate uncompacted graph.  ...  an early draft of the software.  ... 
doi:10.1186/s13059-020-02135-8 pmid:32943081 pmcid:PMC7499882 fatcat:dgrvnmstwrgenby6dcfjirbe3m

Page 5304 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
It is used both to construct span | de Bruijn sequences of a range of linear complexities and to prove non-existence for arbitrary spans.  ...  Upper and lower bounds for the linear complexity of a de Bruijn sequence are established.  ... 

BdBG: a bucket-based method for compressing genome sequencing data with dynamic de Bruijn graphs

Rongjie Wang, Junyi Li, Yang Bai, Tianyi Zang, Yadong Wang
2018 PeerJ  
Compared with existing de Bruijn graph methods, BdBG only stored a list of bucket indexes and bifurcations for the raw read sequences, and this feature can effectively reduce storage space.  ...  In this paper, we propose a novel alignment-free and reference-free compression method, BdBG, which is the first to compress genome sequencing data with dynamic de Bruijn graphs based on the data after  ...  ACKNOWLEDGEMENTS We thank the anonymous reviewers for their insightful comments on earlier versions of this article. ADDITIONAL INFORMATION AND DECLARATIONS  ... 
doi:10.7717/peerj.5611 pmid:30364599 pmcid:PMC6197042 fatcat:sy4vbsqnjffzbnf2zlpoljlmi4
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