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Bisecting de Bruijn and Kautz Graphs
, 1998
"... this paper appeared at The 2nd Colloquium on Structural Information and Communication Complexity (SIROCCO'95), Olympia, Greece, June 1214, 1995. ..."
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this paper appeared at The 2nd Colloquium on Structural Information and Communication Complexity (SIROCCO'95), Olympia, Greece, June 1214, 1995.
Bounds for the bandwidth of the dary de Bruijn graph
, 1993
"... The computation of upper bounds of the bandwidth of graphs is mainly based on the giving of a numbering which achieves these bounds. In [9], Harper proposed such a numbering for the binary hypercube, based on the Hamming weights and binary values of the hypercube vertices. By defining an extended Ha ..."
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Cited by 4 (1 self)
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The computation of upper bounds of the bandwidth of graphs is mainly based on the giving of a numbering which achieves these bounds. In [9], Harper proposed such a numbering for the binary hypercube, based on the Hamming weights and binary values of the hypercube vertices. By defining an extended Hamming weight, this numbering can lead to an equivalent proof for the dary de Bruijn graph. We present in this paper an approach, based on the use of the continuous domain and Laplace's theorem for asymptotically evaluating integrals, which leads to the enumeration of the vertices of same extended Hamming weight in the nonbinary case. This result allows the computation of an upper bound of the bandwidth of the unoriented de Bruijn graph, as well as an upper bound of its vertexbisection when both the diameter and the degree are even.
Congestion and Dilation, Similarities and Differences: a Survey
 In Proc. 7th Intl. Colloquium on Structural Information and Communication Complexity
, 2000
"... We survey general results on congestion and dilation, and their special cases (cyclic) cutwidth and (cyclic) bandwidth, with the emphasis on the similarity and the duality of both parameters. Keywords Bandwidth, Congestion, Cutwidth, Embedding, Dilation 1 Introduction Recently diverse properti ..."
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We survey general results on congestion and dilation, and their special cases (cyclic) cutwidth and (cyclic) bandwidth, with the emphasis on the similarity and the duality of both parameters. Keywords Bandwidth, Congestion, Cutwidth, Embedding, Dilation 1 Introduction Recently diverse properties and invariants of interconnection networks (not only those of parallel machines) have been studied and a lot of interesting results have been shown (e.g. see [16, 36]). One of the important features of an interconnection network is its ability to efficiently simulate programs written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding. Informally, the graph embedding problem is to label the vertices of a "guest" graph (e.g. a communication graph of processes and relations between the processes) G by distinct vertices of a "host" graph (an interconnection network) H. The quality of the embedding corresponding to the efficiency of the sim...
New results on edgebandwidth
 Theoret. Comput. Sci
"... The edgebandwidth problem is an analog of the classical bandwidth problem, in which one has to label the edges of a graph by distinct integers such that the maximum difference of labels of any two incident edges is minimized. We prove tight bounds on the edgebandwidth of hypercube and butterfly gr ..."
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The edgebandwidth problem is an analog of the classical bandwidth problem, in which one has to label the edges of a graph by distinct integers such that the maximum difference of labels of any two incident edges is minimized. We prove tight bounds on the edgebandwidth of hypercube and butterfly graphs and complete kary trees which extend and improve on previous known results. We also provide an improvement on the upper bound for the bandwidth of butterfly. 1