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Latin Hypercubes and Cellular Automata [article]

Maximilien Gadouleau, Luca Mariot
2020 arXiv   pre-print
Further, we derive the number of k-dimensional Latin hypercubes generated by LBCA by counting the number of paths of length k-3 on this de Bruijn graph.  ...  can be described by a specific kind of regular de Bruijn graph induced by the support of the determinant function.  ...  Rows in bold in the table correspond to the vectors of the support of det, which in turn are the vertices of the de Bruijn graph.  ... 
arXiv:2004.07131v1 fatcat:pewo2c6mkjcplm456mct5pv4ty

Dense edge-disjoint embedding of complete binary trees in interconnection networks

S. Ravindran, A.M. Gibbons, M.S. Paterson
2000 Theoretical Computer Science  
We describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shu e-exchange networks and the two-dimensional  ...  We prove that the maximum distance from a leaf to the root of the tree is asymptotically as short as possible in all host graphs except in the case of the shu e-exchange, in which case we conjecture that  ...  , de Bruijn and shu e-exchange graphs.  ... 
doi:10.1016/s0304-3975(00)00066-9 fatcat:zgilbrqsubfbvgyzebbyvajhou

Extension of de Bruijn graph and Kautz graph

Y. Shibata, Y. Gonda
1995 Computers and Mathematics with Applications  
Basic properties of extended de Bruijn graphs and extended Kautz graphs are given and finally several new results on isomorphic factorization of those graphs are given. geywords--Vector system, Extended  ...  de Bruijn graph, Extended Kautz graph, Flowered complete digraph, Isomorphic factorization.  ...  INTRODUCTION Hypercubes, de Bruijn graphs, and Kautz graphs play an important role in computer networks as fundamental models.  ... 
doi:10.1016/0898-1221(95)00146-p fatcat:x6misjhf4zbknltxh56qnkar3m

Product-shuffle networks: toward reconciling shuffles and butterflies

Arnold L Rosenberg
1992 Discrete Applied Mathematics  
Further, algebraic transformations [3] of these large networks yield the smaller, shuffle-oriented bounded-degree "approximations" of the hypercube, most notably the shuffleexchange' [22] and de Bruijn  ...  These networks were constructed with a certain important genre of hypercube algorithm, called ascend-descend algorithms [ 161, in mind and so can emulate the hypercube with little or no slowdown on a large  ...  One noteworthy point is that PS graphs share diameter (exactly) log2 N bvith de Bruijn graphs and hypercubes, although de Bruijn graphs acquire their small diameter with valence 4, while PS graphs have  ... 
doi:10.1016/0166-218x(92)90152-z fatcat:maihv5dfzjf55d33frhcvb5wea

Page 3220 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
In this paper, we focus on undirected de Bruijn networks of radix d and dimension n, denoted by UB(d,n). We first discuss the shortest-path routing problem.  ...  Summary: “De Bruijn graphs, both directed and undirected, have received considerable attention as an architecture for interconnec- tion networks.  ... 

Minimum feedback vertex sets in shuffle-based interconnection networks

Rastislav Královič, Peter Ružička
2003 Information Processing Letters  
In Section 4 we construct a minimum feedback vertex set in shuffle-exchange, binary de Bruijn and ternary Kautz graphs. § 1 © © We apply this theorem to shuffle-exchange, binary de Bruijn, and ternary  ...  Tight upper and lower bounds on the cardinality of minimum feedback vertex sets have been obtained for some hypercube-like networks, such as meshes, tori, butterflies, cube-connected cycles and hypercubes  ...  Figure 2 : 2 Minimum feedback set in a de Bruijn graph of even dimension (DB 4 ).  ... 
doi:10.1016/s0020-0190(02)00504-5 fatcat:vskyikxllfdxfgygl2nwnz7qpa

Bus interconnection networks

Jean-Claude Bermond, Fahir Ö. Ergincan
1996 Discrete Applied Mathematics  
Some of these pointto-point networks can be used in the construction of bus networks. One approach is to consider the dual of the network.  ...  We survey the results obtained on the construction methods that connect a large number of processors in a bus network with given maximum processor degree A, maximum bus size r. and network diameter D.  ...  De Bruijn and Kautz hypergraphs De Bruijn and Kautz hypergraphs are the generalizations of de Bruijn digraphs and Kautz digraphs to directed hypergraphs.  ... 
doi:10.1016/0166-218x(95)00046-t fatcat:2cgwb7ksfndwxmrq5ntzur2gr4

Broadcasting in DMA-bound bounded degree graphs

E. Lazard
1992 Discrete Applied Mathematics  
Nous donnons des bornes inferieures et construisons des reseaux de degre borne permettant une diffusion rapide. Nous utilisons la notion de composition de graphes dans les reseaux de de Bruijn.  ...  Our constructions use the notion of compounding graphs in de Bruijn digraphs. We also obtain asymptotic upper and lower bounds for broadcast time, as the maximum degree increases.  ...  We compound the graph G = (K#'-2m)fi in the de Bruijn digraph B(m3@ -2m)'2,D) for any 1 s ms L(A -2)/2], and distribute the arcs from the de Bruijn digraph so that each vertex of each copy of G is given  ... 
doi:10.1016/0166-218x(92)90147-3 fatcat:lh6zfpzubzfttjsak5lgvggoiu

Page 5121 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
This is in sharp contrast to most other such constructions (including the de Bruijn graph), in which only one graph exists for each N.  ...  A. (1-SC-C); Raghavendra, C.S. (1-SCA-D) Fault-tolerant networks based on the de Bruijn graph. IEEE Trans. Comput. 40 (1991), no. 10, 1167-1174.  ... 

Fault-tolerant de Bruijn and shuffle-exchange networks

J. Bruck, R. Cypher, Ching-Tien Ho
1994 IEEE Transactions on Parallel and Distributed Systems  
In particular, the reconfiguration algorithm for the base-m de Bruijn graph is identical to the one used for the base-2 de Bruijn graph and will not be repeated.  ...  In this paper, we focus on the creation of fault-tolerant de Bruijn and (point-to-point) shuffleexchange graphs.  ...  In our modeling technique we decomposed the memory references of a hierarchical system into as many groups as the number of hierarchy levels in the system.  ... 
doi:10.1109/71.282566 fatcat:i4lh2fnjb5dm7inblbci2vw52m

Different DNA Sequencing Using DNA Graphs: A Study

Abdulaziz M. Alanazi, G. Muhiuddin, Doha A. Al-Balawi, Sovan Samanta
2022 Applied Sciences  
This study aims to investigate the role of DNA sequencing and its representation in the form of graphs in the analysis of different diseases by means of DNA sequencing.  ...  Natural genetic material may shed light on gene expression mechanisms and aid in the detection of genetic disorders.  ...  The algorithm's first draught, on the basis of de Bruijn graphs, was published in [8] , and it was modified further in [9] .  ... 
doi:10.3390/app12115414 fatcat:alljeotdcfgilld5iyo52r34oi

Page 4929 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
This allows him to derive an upper bound on the broadcast time of the symmetric digraph obtained from the de Bruijn digraph, and thus of the undirected de Bruijn graph, which is asymptotically optimal.  ...  This leads to the first efficient gossiping protocols on the shuffle-exchange and on undirected de Bruijn graphs. More interesting than the results on these particular networks are the methods used.  ... 

Cartesian products of graphs as spanning subgraphs of de Bruijn graphs [chapter]

Thomas Andreae, Michael Nölle, Gerald Schreiber
1995 Lecture Notes in Computer Science  
Gm (m 2) of we apply our results to obtain embeddings of relatively small dilation of popular processor networks (as tori, meshes and hypercubes) into de Bruijn graphs of xed small base.  ...  We close with a remark on embeddings into base C de Bruijn graphs where C is a xed constant.  ...  We close with a remark on embeddings into de Bruijn graphs of small xed base and brie y report on experimental results.  ... 
doi:10.1007/3-540-59071-4_44 fatcat:3s6v33mdgfasrmmppeoi7ftld4

Embedding Cartesian Products of Graphs into de Bruijn Graphs

Thomas Andreae, Michael Nölle, Gerald Schreiber
1997 Journal of Parallel and Distributed Computing  
As corollaries, we obtain results improving previous results of Heydemann, Opatrny, and Sotteau (1994) on embedding grids and tori into de Bruijn graphs.  ...  For 2{dimensional de Bruijn graphs D = D B (2), we present a theorem stating that certain structural assumptions on the factors G 1 ; : : :; G m ensure that G 1 : : : G m is a spanning subgraph of D.  ...  In 12] results on the embedding of multidimensional tori into de Bruijn graphs were presented. (For de nitions, see Section 2.)  ... 
doi:10.1006/jpdc.1997.1384 fatcat:klgwbyvscvc7nfhrettfmfr4vu

Page 7944 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
In this paper, we report on a coil searching computer program which established that 48 is the maximum length of a coil in the hypercube of dimension 7.”  ...  (N-BERG-I; Bergen); Mykkeltveit, Johannes On the classification of de Bruijn sequences. (English summary) Discrete Math. 148 (1996), no. 1-3, 65-83.  ... 
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