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Construction of de Bruijn sequences of minimal complexity
1984
IEEE Transactions on Information Theory
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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
1985
Journal of combinatorial theory. Series A
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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
1999
Journal of combinatorial theory. Series A
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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]
2013
Lecture Notes in Computer Science
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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]
2005
arXiv
pre-print
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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
1996
Journal of combinatorial theory. Series A
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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]
2006
Lecture Notes in Computer Science
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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
2001
Discrete Mathematics
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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]
2019
biorxiv/medrxiv
pre-print
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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
2013
Algorithms for Molecular Biology
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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]
2019
bioRxiv
pre-print
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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
2022
IEEE Access
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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
2020
Genome Biology
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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
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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
2018
PeerJ
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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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