Group Action Graphs and Parallel Architectures

Annexstein, Fred S.; Baumslag, Marc; Rosenberg, Arnold L.

doi:10.1137/0219037

Cited by 175 publications

(145 citation statements)

References 17 publications

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“…19]). In addition, there is also a strong structural relationship to the deBruijn, shu e-exchange, and butter y networks 1,10]. Hence, the e cient implementation of algorithms on CCC networks (of xed size) is of importance.…”

Section: Proposition 1 20]mentioning

confidence: 99%

“…We will see later on Proof 4 bitstrings, and in the second case, we choose the last ñ 4 4 bitstrings. To guarantee that these bitstrings are di erent, we have to check that ñ 1 4 + ñ 4 4 2 n?2 : But this is true for l k > 5 3 . ] c) The nodes from f(h(i); ); (h(i) + 1; ) j 2 f0; 1g n g which have not been assigned a value for d in a) and b) are assigned arbitrary values from fr(i); r(i)+ 1g such that the requirements for n 2 and n 3 are ful lled.…”

Section: Proposition 1 20]mentioning

confidence: 99%

“…For low dilation, the values of (0) f0; 1gg can be allocated balancedly on the complete host cycle C a (0) a (1) :::a (k?1) , a (0) ; a (1) ; : : : ; a (k?1) 2 f0; 1g, while maintaining dilation 1 at the same time.…”

Section: Proposition 1 20]mentioning

confidence: 99%

“…The main new technical contribution will be to show that the guest nodes f( (i) + 1; a 0 a 1 : : : a l?1 ); ( (i) + 2; a 0 a 1 : : : a l?1 ) j a (0) ; a (1) ; : : : ; a (l?k?1) 2 f0; 1gg can be allocated in an appropriate way among the host nodes f(j; a (0) a (1) : : : a (k?1) ) j j 2 fi ? 1; i; i + 1; i + 2gg for 0 i < k ?…”

Section: Proposition 1 20]mentioning

confidence: 99%

See 3 more Smart Citations

Improved Compressions of Cube-Connected Cycles Networks

Klasing

1998

Graph-Theoretic Concepts in Computer Science

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We present a new technique for the embedding of large cube-connected cycles networks (CCC) into smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a xed size. Using the new embedding strategy, we show that the CCC of dimension l can be embedded into the CCC of dimension k with dilation 1 and optimum load for any k; l 2 IN, k 8, such that 5 3 + c k < l k 2, c k = 4k + 3 3 2 2=3k , thus improving known results. Our embedding technique also leads to improved dilation 1 embeddings in the case 3 2 < l k 5 3 + c k .

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Section: Proposition 1 20]mentioning

confidence: 99%

Section: Proposition 1 20]mentioning

confidence: 99%

Section: Proposition 1 20]mentioning

confidence: 99%

Section: Proposition 1 20]mentioning

confidence: 99%

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Improved Compressions of Cube-Connected Cycles Networks

Klasing

1998

Graph-Theoretic Concepts in Computer Science

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“…It is known that Cayley graphs are excellent models for interconnection networks [1,3]. Many well-known and practically useful interconnection networks are Cayley graphs.…”

Section: Cayley-graph Network Modelsmentioning

confidence: 99%

Cayley graphs as models of deterministic small-world networks

Xiao

Parhami

2006

Information Processing Letters

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Many real networks, including those in social, technological, and biological realms, are small-world networks. The two distinguishing characteristics of small-world networks are high local clustering and small average internode distance. A great deal of previous research on small-world networks has been based on probabilistic methods, with a rather small number of researchers advocating deterministic models. In this paper, we further the study of deterministic small-world networks and show that Cayley graphs may be good models for such networks. Small-world networks based on Cayley graphs possess simple structures and significant adaptability. The Cayley-graph model has pedagogical value and can also be used for designing and analyzing communication and the other real networks.

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Orienting split-stars and alternating group graphs

Cheng

Lipman

2000

Networks

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Akers et al. proposed an interconnection topology, the star graph, as an alternative to the popular n‐cube. Cheng et al. proposed the split‐star as an alternative to the star graph and a companion graph to the alternating group graph proposed by Jwo et al. Star graphs, alternating group graphs, and split‐stars are advantageous over n‐cubes in many aspects. Day and Tripathi proposed an assignment of directions to the edges of the star graph and showed that the resulting directed graph is strongly connected and has a simple routing algorithm. In this paper, we give simple routing algorithms for a proposed orientation of alternating group graphs and split‐stars. The resulting directed graphs are not only strongly connected but they have maximal arc‐fault tolerance and a small diameter. © 2000 John Wiley & Sons, Inc.

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Group Action Graphs and Parallel Architectures

Cited by 175 publications

References 17 publications

Improved Compressions of Cube-Connected Cycles Networks

Improved Compressions of Cube-Connected Cycles Networks

Cayley graphs as models of deterministic small-world networks

Orienting split-stars and alternating group graphs

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