Balanced de Bruijn Sequences

Marcovich, Sagi; Etzion, Tuvi; Yaakobi, Eitan

doi:10.1109/isit45174.2021.9517873

Cited by 6 publications

(5 citation statements)

References 31 publications

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“…By Definition 1 and Lemma 1 we know that |S i−1 (w)| = d i−1 and that, either S k,i (v) = ∅ or |S k,i (v)| = |S k (v)| = d k . Therefore, from (21) we conclude that…”

Section: Proof Of Statement (4) Of Propositions 3 Andmentioning

confidence: 77%

See 1 more Smart Citation

Distance-layer structure of the De Bruijn and Kautz digraphs: analysis and application to deflection routing (with examples and remarks)

Fàbrega¹,

Martí-Farré²,

Muñoz³

2022

Preprint

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In this paper, we present a detailed study of the reach distance-layer structure of the De Bruijn and Kautz digraphs, and we apply our analysis to the performance evaluation of deflection routing in De Bruijn and Kautz networks. Concerning the distance-layer structure, we provide explicit polynomial expressions, in terms of the degree of the digraph, for the cardinalities of some relevant sets of this structure. Regarding the application to defection routing, and as a consequence of our polynomial description of the distance-layer structure, we formulate explicit rational expressions, in terms of the degree of the digraph, for some probabilities of interest in the analysis of this type of routing.De Bruijn and Kautz digraphs are fundamental examples of digraphs on alphabet and iterated line digraphs. If the topology of the network under consideration corresponds to a digraph of this type, we can perform, in principle, a similar vertex layer description.

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“…By Definition 1 and Lemma 1 we know that |S i−1 (w)| = d i−1 and that, either S k,i (v) = ∅ or |S k,i (v)| = |S k (v)| = d k . Therefore, from (21) we conclude that…”

Section: Proof Of Statement (4) Of Propositions 3 Andmentioning

confidence: 77%

“…Despite being known for a long time, active research is still going on on De Bruijn and Kautz digraphs B(d, D) and K(d, D) [4,7,17,18], both in graph theory [5,9,15,20] and in network engineering [12,21,25,28]. This paper is concerned with deflection routing in these kind of networks.…”

Section: Introductionmentioning

confidence: 99%

Distance-layer structure of the De Bruijn and Kautz digraphs: analysis and application to deflection routing (with examples and remarks)

Fàbrega¹,

Martí-Farré²,

Muñoz³

2022

Preprint

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show abstract

“…Despite being known for a long time, active research is still going on on De Bruijn and Kautz digraphs

B\left(d,D\right)

and

K\left(d,D\right)

[3, 9, 20, 21], both in graph theory [4, 10, 18, 23] and in network engineering [14, 24, 28]. Those digraphs have been proposed as topologies for optical networks (see for instance [5, 7, 30]).…”

Section: Introductionmentioning

confidence: 99%

Distance‐layer structure of the De Bruijn and Kautz digraphs: Analysis and application to deflection routing

2023

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In this article, we present a detailed study of the reach distance‐layer structure of the De Bruijn and Kautz digraphs, and we apply our analysis to the performance evaluation of deflection routing in De Bruijn and Kautz networks. Concerning the distance‐layer structure, we provide explicit polynomial expressions, in terms of the degree of the digraph, for the cardinalities of some relevant sets of this structure. Regarding the application to defection routing, and as a consequence of our polynomial description of the distance‐layer structure, we formulate explicit expressions, in terms of the degree of the digraph, for some probabilities of interest in the analysis of this type of routing. De Bruijn and Kautz digraphs are fundamental examples of digraphs on alphabet and iterated line digraphs. If the topology of the network under consideration corresponds to a digraph of this type, we can perform, in principle, a similar vertex layer description.

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“…We can view it as a constrained version of a de Bruijn sequence. On the theoretical side, there are works on several kinds of constrained de Bruijn sequences, including balanced de Bruijn sequence [41], and de Bruijn sequence with constrained language [44,48]. In addition, we note that the s-RLL code has been well-studied [26,25] and the universal cycles for constrained words have attracted some attention recently [21,49].…”

Section: Run-length Limited De Bruijn Sequencementioning

confidence: 99%

“…In this work, we demonstrate that Conjecture A is true for an infinite set of parameters. In the range n 2 [2,50] (39,20), (40,21), (40,22), (41,21), (41,22), (42,22), (46,25), (47,25), (47,26), (48,25), (48,26), (49,25), (49,26), (50,25), (50,26), (50,27)}.…”

Section: The Case N/2 < D < 2n/3mentioning

confidence: 99%

Applications of combinatorics in coding theory

Dao¹

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Balanced de Bruijn Sequences

Cited by 6 publications

References 31 publications

Distance-layer structure of the De Bruijn and Kautz digraphs: analysis and application to deflection routing (with examples and remarks)

Distance-layer structure of the De Bruijn and Kautz digraphs: analysis and application to deflection routing (with examples and remarks)

Distance‐layer structure of the De Bruijn and Kautz digraphs: Analysis and application to deflection routing

Applications of combinatorics in coding theory

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