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Construction of de Bruijn sequences of minimal complexity

1984
*
IEEE Transactions on Information Theory
*

It is well known that the linear

doi:10.1109/tit.1984.1056965
fatcat:s4vvhdoa4rfzhgs3plxxmpwi3m
*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. ...##
###
On the distribution of de bruijn sequences of low complexity

1985
*
Journal of combinatorial theory. Series A
*

First, we give examples

doi:10.1016/0097-3165(85)90074-3
fatcat:t3ggqqu2sfa5lfu6xhsafonnzi
*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. ...##
###
On the Minimum Linear Complexity of de Bruijn Sequences over Non-prime Finite Fields

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

doi:10.1006/jcta.1998.2920
fatcat:vw6tvc6spba23pb5vixaxyvwbu
*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*...##
###
Cryptographically Strong de Bruijn Sequences with Large Periods
[chapter]

2013
*
Lecture Notes in Computer Science
*

s technique for producing

doi:10.1007/978-3-642-35999-6_8
fatcat:2xvvxnx4rne4vknaztoa5h36ia
*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] . ...##
###
Minimal Eulerian trail in a labeled digraph
[article]

2005
*
arXiv
*
pre-print

We also show an application

arXiv:cs/0505036v1
fatcat:wg3yrrcqmneg3dn46oq7owa26i
*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. ...##
###
Permutation Polynomials, de Bruijn Sequences, and Linear Complexity

1996
*
Journal of combinatorial theory. Series A
*

The connection is used both to

doi:10.1006/jcta.1996.0088
fatcat:quu2lgo2ivdsbeytymsnikowgi
*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. ...##
###
Minimal Eulerian Circuit in a Labeled Digraph
[chapter]

2006
*
Lecture Notes in Computer Science
*

We also show an application

doi:10.1007/11682462_67
fatcat:ofrxbv7srjckdiyixs337ef46m
*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. ...##
###
De Bruijn sequences with efficient decoding algorithms

2001
*
Discrete Mathematics
*

A

doi:10.1016/s0012-365x(00)00117-5
fatcat:kau7udrrgnaqxjr3quribfpney
*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. ...##
###
Indexing De Bruijn graphs with minimizers
[article]

2019
*
biorxiv/medrxiv
*
pre-print

Moreover, it can be efficiently built from the

doi:10.1101/546309
fatcat:szs2yd455bfptmwumelz5yiaka
*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. ...##
###
Space-efficient and exact de Bruijn graph representation based on a Bloom filter

2013
*
Algorithms for Molecular Biology
*

The

doi:10.1186/1748-7188-8-22
pmid:24040893
pmcid:PMC3848682
fatcat:6ltoll4ztrgh3nwjxtntsezwym
*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. ...##
###
Bifrost – Highly parallel construction and indexing of colored and compacted de Bruijn graphs
[article]

2019
*
bioRxiv
*
pre-print

Results: We present a new parallel and memory efficient algorithm enabling the direct

doi:10.1101/695338
fatcat:a7wnmn7ovnav3h6tw6sysrbkby
*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. ...##
###
Graph theoretical Strategies in De Novo Assembling

2022
*
IEEE Access
*

INDEX TERMS Combinatorial data structures,

doi:10.1109/access.2022.3144113
fatcat:iajrk3fq6jhbfel7apoowu3v2m
*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] ...##
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Bifrost: highly parallel construction and indexing of colored and compacted de Bruijn graphs

2020
*
Genome Biology
*

Memory consumption

doi:10.1186/s13059-020-02135-8
pmid:32943081
pmcid:PMC7499882
fatcat:dgrvnmstwrgenby6dcfjirbe3m
*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. ...##
###
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

2018
*
PeerJ
*

Compared with existing

doi:10.7717/peerj.5611
pmid:30364599
pmcid:PMC6197042
fatcat:sy4vbsqnjffzbnf2zlpoljlmi4
*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 ...
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