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17
Methods and problems of communication in usual networks
, 1994
"... This paper is a survey of existing methods of communication in usual networks. We particularly study the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the star graph, the shuffleexchange graph, and the butterfly graph. Two ..."
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Cited by 110 (11 self)
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This paper is a survey of existing methods of communication in usual networks. We particularly study the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the star graph, the shuffleexchange graph, and the butterfly graph. Two different models of communication time are analysed, namely the constant model and the linear model. Other constraints like fullduplex or halfduplex links, processorbound, DMAbound or linkbound possibilities are separately studied. For each case we give references, upper bound (algorithms) and lower bounds. We have also proposed improvements or new results when possible. Hopefully, optimal results are not always known and we present a list of open problems.
Matrix multiplication on hypercubes using full bandwidth and constant storage
 In The Sixth Distributed Memory Computing Conference Proceedings
, 1991
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Hamilton cycle decomposition of the Butterfly network
, 1996
"... In this paper, we prove that the wrapped Butterfly graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2. ..."
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Cited by 4 (2 self)
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In this paper, we prove that the wrapped Butterfly graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2.
Oblivious Gossiping on Tori
 Journal of Algorithms
"... Nearoptimal gossiping algorithms are given for two and higher dimensional tori assuming the fullport storeandforward communication model. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with an adaptive routing pattern. In contrast, the PUs in our algo ..."
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Cited by 4 (2 self)
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Nearoptimal gossiping algorithms are given for two and higher dimensional tori assuming the fullport storeandforward communication model. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with an adaptive routing pattern. In contrast, the PUs in our algorithm forward the received packets always in the same way. We thus achieve almost the same performance with patterns that might be hardwired.
Revisiting Hamiltonian Decomposition of the Hypercube
 SBCCI2000  XIII Symposium on Integrated Circuits and System Design
, 2000
"... this paper we study a useful namely the Hamiltonian decomposition, i.e. the partitioning of its edge set into Hamiltonian cycles. It is known that there are bn=2c disjoint Hamiltonian cycles on a binary ncube. The proof of this result, however, does not give rise to any simple construction algorith ..."
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Cited by 3 (0 self)
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this paper we study a useful namely the Hamiltonian decomposition, i.e. the partitioning of its edge set into Hamiltonian cycles. It is known that there are bn=2c disjoint Hamiltonian cycles on a binary ncube. The proof of this result, however, does not give rise to any simple construction algorithm of such cycles. In a previous work Song presents ideas towards a simple method to this problem. First decompose the hypercube into cycles of length 16, C 16 , and then apply a merge operator to join the C 16 cycles into larger Hamiltonian cycles. The case of dimension n = 6 (a 64node hypercube) is illustrated. He conjectures the method can be generalized for any even n. In this paper, we generalize the rst phase of that method for any even n and prove its correctness. Also we show four possible merge operators for the case of n = 8 (a 256node hypercube). This result can be viewed as a step toward the general merge operator, thus proving the conjecture
TimeIndependent Gossiping on FullPort Tori
 MaxPlanck Institut fr Informatik
, 1998
"... Nearoptimal gossiping algorithms are given for two and higher dimensional tori. It is assumed that the amount of data each PU contributes is so large that startup time may be neglected. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with a timedependent r ..."
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Cited by 3 (2 self)
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Nearoptimal gossiping algorithms are given for two and higher dimensional tori. It is assumed that the amount of data each PU contributes is so large that startup time may be neglected. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with a timedependent routing pattern. In all steps of our algorithms, the PUs forward the received packets in the same way.
Hamilton circuits in directed Butterfly networks
 RESEARCH REPORT #2925  THEME 1, INRIA SOPHIA ANTIPOLIS
, 1996
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Hamilton circuits in the directed wrapped Butterfly network
, 1996
"... In this paper, we prove that the wrapped Butterfly digraph ~ WBF(d;n) of degree d and dimension n contains at least d \Gamma 1 arcdisjoint Hamilton circuits, answering a conjecture of D. Barth. We also conjecture that ~ WBF(d;n) can be decomposed into d Hamilton circuits, except for {d = 2 and n = ..."
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Cited by 3 (0 self)
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In this paper, we prove that the wrapped Butterfly digraph ~ WBF(d;n) of degree d and dimension n contains at least d \Gamma 1 arcdisjoint Hamilton circuits, answering a conjecture of D. Barth. We also conjecture that ~ WBF(d;n) can be decomposed into d Hamilton circuits, except for {d = 2 and n = 2}, {d = 2 and n = 3} and {d = 3 and n = 2}. We show that it suffices to prove the conjecture for d prime and n = 2. Then, we give such a Hamilton decomposition for all primes less than 12000 by a clever computer search, and so, as a corollary, we have a Hamilton decomposition of ~ WBF(d;n) for any d divisible by a number q, with 4 q 12000.
Gossiping Large Packets on FullPort Tori
 In Proc. EuroPar 1998 Parallel Processing, volume 1470 of LNCS
, 1998
"... Nearoptimal gossiping algorithms are given for two and higher dimensional tori. It is assumed that the amount of data each PU is contributing is so large, that startup time may be neglected. For twodimensional tori, an earlier algorithm achieved optimality in an intricate way, with a timedepend ..."
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Cited by 2 (2 self)
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Nearoptimal gossiping algorithms are given for two and higher dimensional tori. It is assumed that the amount of data each PU is contributing is so large, that startup time may be neglected. For twodimensional tori, an earlier algorithm achieved optimality in an intricate way, with a timedependent routing pattern. In our algorithms, in all steps, the PUs forward the received packets in the same way.
Towards a simple construction method for Hamiltonian decomposition of the hypercube
, 1994
"... . We consider the problem of Hamiltonian decomposition on the hypercube. It is known that there exist bn=2c edgedisjoint Hamiltonian cycles on a binary ncube. However, there are still no simple algorithms to construct such cycles. We present some promising results that may lead to a very simple me ..."
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Cited by 1 (1 self)
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. We consider the problem of Hamiltonian decomposition on the hypercube. It is known that there exist bn=2c edgedisjoint Hamiltonian cycles on a binary ncube. However, there are still no simple algorithms to construct such cycles. We present some promising results that may lead to a very simple method to obtain the Hamiltonian decomposition. The binary ncube is equivalent to the Cartesian product of cycles of length four (C4 \Theta C4 : : : \Theta C4 ). Case n = 4 is trivial. For the case n = 6, we first partition the set of edges of the C 4 \Theta C 4 \Theta C 4 into 12 disjoint cycles of length 16. We then present an operator to merge the cycles to produce the desired Hamiltonian cycles. In general the edge set of n=2 products C 4 \Theta C 4 : : : \Theta C 4 , can be partitioned into n2 n =32 disjoint cycles of length 16. It remains to formalize the merge operator in the general case. 1. Introduction The problem of finding edgedisjoint cycles on a hypercube can be important i...