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Small congestion embedding of graphs into hypercubes

Akira Matsubayashi, Shuichi Ueno
1999 Networks  
We consider the problem of embedding graphs into hypercubes with minimal congestion.  ...  The latter is the first result that shows a simple embedding of a binary tree into an optimal sized hypercube with explicit small congestion of 5.  ...  The research is a part of CAD21 project at TIT.  ... 
doi:10.1002/(sici)1097-0037(199901)33:1<71::aid-net5>3.0.co;2-3 fatcat:p5cvuonwebcfpgggg37k7rc5ca

Efficient Embeddings into Hypercube-like Topologies

V. Heun
2003 Computer journal  
In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs.  ...  Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids.  ...  THE EMBEDDING In this section, we construct embeddings of arbitrary graphs into (k, h, o, λ)-trees provided the graphs have small bisectors.  ... 
doi:10.1093/comjnl/46.6.632 fatcat:ywukz3e7n5defl5b6fzf3s5ime

Page 6610 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
The latter is the first result that shows a simple embedding of a binary tree into an optimal-sized hypercube with an explicit small congestion of 5.  ...  Summary: “We consider the problem of embedding graphs into hypercubes with minimal congestion. Y. M. Kim and T. H. Lai [J.  ... 

Optimal Dynamic Embeddings of Complete Binary Trees into Hypercubes

Volker Heun, Ernst W. Mayr
2001 Journal of Parallel and Distributed Computing  
Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into a hypercube does not provide any hint on how this embedding can be extended if each leaf spawns two new  ...  In this paper, we present simple dynamic embeddings of double-rooted complete binary trees into hypercubes which do not suffer from this disadvantage.  ...  The congestion of an embedding is the maximal congestion over all edges in H. The smallest hypercube into which a graph can be embedded one-to-one is called its optimal hypercube.  ... 
doi:10.1006/jpdc.2001.1734 fatcat:baaz4bl2q5betcondlgiglbvvy

One-to-One Embedding between Hyper Petersen and Petersen-Torus Networks [chapter]

Jung-Hyun Seo, Moon-Suk Jang, EungKon Kim, Kyeong-Jin Ban, NamHoon Ryu, HyeongOk Lee
2009 Communications in Computer and Information Science  
Hyper Petersen ‫ܲܪ‬ మ మ ାଷ was embedded into Petersen-Torus PT(n,n) with expansion 1, dilation 1.5n+2, and congestion 5n.  ...  The embedding algorithm was designed for expansion 1, and congestion and dilation are in proportion to O(n) owing to the aspect of Hyper Petersen that the degree increases.  ...  In study [2] , 11-dimensional Hypercube was embedded into 32×64 mesh at dilation 32 and congestion 57, and smaller Hypercube and meshes were embedded.  ... 
doi:10.1007/978-3-642-10549-4_16 fatcat:7p66iobn4fcu7k6hzsrfckz3h4

Embedding hyperpyramids into hypercubes

C.-T. Ho, S. L. Johnsson
1994 IBM Journal of Research and Development  
The dilation of the embedding is d + 1, with a congestion of O(2').  ...  We also present embeddings of a hyperpyramid &k, d ) together with 2d -2 hyperpyramids &k -1, d ) such that only one hypercube node is unused.  ...  Acknowledgment We thank David Greenberg for his comments on an early draft of this paper, and Peter Corbett, who provided the  ... 
doi:10.1147/rd.381.0031 fatcat:apitirpaord7fhwghevfw4adpm

Efficient Embeddings of Trees in Hypercubes

Sandeep N. Bhatt, Fan R. K. Chung, F. Thomson Leighton, Arnold L. Rosenberg
1992 SIAM journal on computing (Print)  
In fact, the proof shows that every bounded-degree graph with an O(1)-separator can be embedded in a hypercube of the same size with dilation and congestion both O(1).  ...  one of embedding the "data-dependency graph" underlying an algorithm within the processor interconnection graph.  ...  Thnks to David Greenberg for helpful discussions and for his careful reading of the manuscript. Thanks also to Lennart Johnsson for early suggestions.  ... 
doi:10.1137/0221012 fatcat:kf2lk5vssfculcilr7saxvolcq

Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes [article]

R. Sundara Rajan, Thomas Kalinowski, Sandi Klavžar, Hamid Mokhtar, T.M. Rajalaxmi
2018 arXiv   pre-print
In this paper, lower bounds for the dilation, wirelength, and edge congestion of an embedding of a graph into a hypercube are proved.  ...  Applying these results, the dilation and wirelength of embedding of certain complete multipartite graphs, folded hypercubes, wheels, and specific Cartesian products are computed.  ...  The hypercube embedding problem is the problem of mapping a communication graph into a hypercube multiprocessor.  ... 
arXiv:1807.06787v2 fatcat:mi3xjq66vjdx3cvryt6nhdozs4

Embeddings Between Hypercubes and Hypertrees

R. Sundara Rajan, Paul Manuel, Indra Rajasingh
2015 Journal of Graph Algorithms and Applications  
Also, we compute the exact wirelength of the embedding of the r-dimensional hypercube Q r into the rooted hypertree RHT (r), r ≥ 2.  ...  Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures.  ...  Arockiaraj, Department of Mathematics, Loyola College, Chennai, India for his fruitful suggestions.  ... 
doi:10.7155/jgaa.00363 fatcat:xfc2ndw2tnb3hpu2drx4pypqsq

Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

Volker Heun, Ernst W. Mayr
2002 Journal of Algorithms  
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube.  ...  This is the first time that embeddings of graphs with a highly irregular structure into hypercubes are investigated.  ...  Our method leads to an embedding of a graph G into the hypercube with dilation 2k + o + 2. The embedding of the graph G into the k h o -tree will be performed as follows.  ... 
doi:10.1006/jagm.2002.1217 fatcat:j2udl5lcufh3jekk54aax4upue

Embedding graphs with bounded treewidth into optimal hypercubes [chapter]

Volker Heun, Ernst W. Mayr
1996 Lecture Notes in Computer Science  
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube.  ...  This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated.  ...  Thus, an embedding of a graph G into its optimal hypercube has expansion less than two.  ... 
doi:10.1007/3-540-60922-9_14 fatcat:olbl6l2tunatjb7nsecjzosdi4

Page 5137 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Various ways of embedding trees into hypercubes have been explored in the litera- ture.  ...  An embedding of a guest graph G into a host graph H is a one- to-one mapping of the vertices of G, V(G), into the vertices of H, V (A), together with a mapping of the edges of G into simple paths of H  ... 

Efficient Dynamic Embeddings of Binary Trees into Hypercubes

Volker Heun, Ernst W. Mayr
2002 Journal of Algorithms  
Because of a known lower bound, any such algorithm must use either randomization or migration, i.e., remapping of tree vertices, to obtain an embedding of trees into hypercubes with small dilation, load  ...  From this construction, a dynamic embedding of large binary trees into hypercubes is derived which achieves dilation of at most 6 and nearly optimal load.  ...  There exists a one-to-one embedding of F into its optimal hypercube with dilation at most 9 and constant node-congestion.  ... 
doi:10.1006/jagm.2002.1218 fatcat:aq7ibim4jzfl3e73n2auoxtx2i

Page 421 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
In this paper we obtain (1) unit expansion embeddings of a variety of multidimensional grids, (2) dilation 1,2,3 and 4 embeddings of hypercubes, and (3) hier- archical and greedy spanning trees to support  ...  “In emulations of separable graphs by cell trees, the node as- signment that ensures small dilation is derived from the separator- based decomposition of guest graphs.  ... 

Supporting the hypercube programming model on mesh architectures

Thomas M. Stricker
1992 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92  
We outline the criteria used to evaluate graph embeddings for mapping supercomputer communication networks.  ...  During the design effort of these building blocks, we developed and analyzed a new technique to support a hypercube network embedded onto a two dimensional torus.  ...  I am grateful to all of them particularly to Thomas Gross, H.T. Kung, Guy Blelloch and Dave O'Hallaron.  ... 
doi:10.1145/140901.140917 dblp:conf/spaa/Stricker92 fatcat:ty7dwp7qgbeafoz5cmxtrabbim
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