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Improved book-embeddings of incomplete hypercubes

Toru Hasunuma
2009 Discrete Applied Mathematics  
In this paper, we show that any incomplete hypercube with, at most, 2 n + 2 n−1 + 2 n−2 vertices can be embedded in n − 1 pages for all n ≥ 4.  ...  For the case n ≥ 4, this result improves Fang and Lai's result that any incomplete hypercube with, at most, 2 n + 2 n−1 vertices can be embedded in n − 1 pages for all n ≥ 2.  ...  Acknowledgments The author is grateful to the referees for their invaluable suggestions and comments that significantly improved the presentation of the paper.  ... 
doi:10.1016/j.dam.2008.10.008 fatcat:oq64mtmeargsnewktqljcqd3my

Embedding of tree networks into hypercubes

Angela Y Wu
1985 Journal of Parallel and Distributed Computing  
The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter.  ...  Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube only with large expansion  ...  relations are preserved.  ... 
doi:10.1016/0743-7315(85)90026-7 fatcat:x6sbsgxkhbf6rblz3nknyqopcu

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

DHT-based Functionalities Using Hypercubes [chapter]

José I. Alvarez-Hamelin, Aline C. Viana, Marcelo D. de Amorim
2006 IFIP International Federation for Information Processing  
In this paper, we propose to increase the number of candidate paths by using incomplete hypercubes.  ...  We will see that this solution can cover a wide range of applications by adapting to the dynamics of the network.  ...  Motivated by these observations, in this paper, we propose to use incomplete hypercubes instead of trees.  ... 
doi:10.1007/978-0-387-34738-7_12 fatcat:obvswax7szgordmkphf53ljqsq


2012 Journal of Interconnection Networks (JOIN)  
estimation of lower bounds. 5, 6 Graph embeddings have been well studied for binary trees into paths, 4 binary trees into hypercubes, 2,7 complete binary trees into hypercubes, 8 incomplete hypercube in  ...  Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks.  ...  network. 1, 2 The quality of an embedding can be measured by certain cost criteria.  ... 
doi:10.1142/s0219265912500041 fatcat:safdiwolbjdh5kcwa2tojz5uie

Embeddings into Hyper Petersen Networks: Yet Another Hypercube-Like Interconnection Topology

Sajal K. Das, Sabine Öhring, Amit K. Banerjee
1995 VLSI design (Print)  
The versatility of the hyper Petersen networks is emphasized by embedding rings, meshes, hypercubes and several tree-related topologies into it.  ...  Contrary to the hypercubes, rings of odd lengths, and a complete binary tree of height n permit subgraph embeddings in HP,.  ...  Acknowledgments We are grateful to the anonymous referees and the Guest Editor for their helpful comments which improved the quality of this paper.  ... 
doi:10.1155/1995/95759 fatcat:fcf2kj52arefpiwp3yhqlsde74

Fault-Tolerant Optimal Broadcast Algorithm For The Hypercube Topology

Lokendra Singh Umrao, Ravi Shankar Singh
2015 Zenodo  
This paper presents an optimal broadcast algorithm for the hypercube networks. The main focus of the paper is the effectiveness of the algorithm in the presence of many node faults.  ...  For the optimal solution, our algorithm builds with spanning tree connecting the all nodes of the networks, through which messages are propagated from source node to remaining nodes.  ...  Any process in hypercube topology can be the root. We present a new way of construction of optimal spanning tree and show its strong relation with the binomial tree.  ... 
doi:10.5281/zenodo.1105517 fatcat:rn6njqdtvvfcfn4a3ga2z3ltfa

HyperCast: A Protocol for Maintaining Multicast Group Members in a Logical Hypercube Topology [chapter]

Jörg Liebeherr, Tyler K. Beam
1999 Lecture Notes in Computer Science  
We use measurement experiments of an implementation of the protocol on a networked computer cluster to quantitatively assess the performance of the protocol for multicast group sizes up to 1024 members  ...  Recently, we proposed the use of a control topology, which organizes multicast group members in a logical n-dimensional hypercube, and transmits all control information along the edges of the hypercube  ...  For example, we plan to use the tree embedding algorithm from Section 3 to provide ARQ error control.  ... 
doi:10.1007/978-3-540-46703-8_5 fatcat:zwrhb5kk7vha7c47gsxzuclssu

Balanced spanning trees in complete and incomplete star graphs

Tzung-Shi Chen, Yu-Chee Tseng, Jang-Ping Sheu
1996 IEEE Transactions on Parallel and Distributed Systems  
In this paper, we show how to construct in a complete star graph an asymptotically balanced spanning tree, and in an incomplete star graph a near-balanced spanning tree.  ...  Efficiently solving the personalized broadcast problem in an interconnection network typically relies on finding an appropriate spanning tree in the network.  ...  The star graph has been considered as an attractive alternative to the widely accepted hypercube as the network architecture for parallel processing.  ... 
doi:10.1109/71.508251 fatcat:5ep55f6ubveazfaxuxbs7oy2c4

Implementation and performance analysis of parallel assignment algorithms on a hypercube computer

B. A. Carpenter, N. J. Davis
1988 Proceedings of the third conference on Hypercube concurrent computers and applications -  
His method used a tree structure embedded into the hypercube interconnection network that was used to search the problem solution space [Mra86].  ...  A mesh structure was embedded into the hypercube network in order to match 0 the structure of the simulated annealing algorithm.  ...  Additional Results This appendix lists all of the remaining results of the implementat ions described in this report.  ... 
doi:10.1145/63047.63077 fatcat:wjluoizfnzhlfitgl2dpwezsde

Tolerating faults in injured hypercubes using maximal fault-free subcube-ring

Yuh-Shyan Chen, Jang-Ping Sheu
1997 Parallel Computing  
Other application algorithms with the free-dimension approach [20], such as embedding rings and meshes [27] , embedding binary tree [28] , and a prefix computation [21] , have been successfully developed  ...  A different but related approach, which is to identify the maximal incomplete subcube, is proposed by Chen and Tzeng [13] by using a reject-region concept.  ...  It is known that an N-node ring can be on-to-one embedded with dilation 3 in any connected N-node network [5] .  ... 
doi:10.1016/s0167-8191(96)00056-7 fatcat:dxmlgnzuundrtjgriyetotd3oy

Fully normal algorithms for incomplete hypercubes

V.K. Prabhala, N.A. Sherwani
[1991] Proceedings. The Fifth International Parallel Processing Symposium  
Incomplete and Composite hypercubes help remove th e exponential node(and hence cost) constraint. In this thesis we establish the equality of m-node composite and incom plete hypercubes.  ...  However, the num ber of nodes m in a hypercube is a power of 2, 2d, where d is the dimension of the hypercube.  ...  In embedding term inology it can be called a "dilation-one-expansion-one" embedding.  ... 
doi:10.1109/ipps.1991.153770 dblp:conf/ipps/PrabhalaS91 fatcat:tzikjfnxx5gvdexvcc4m55gnqe

Parallel thinning algorithms and their implementation on hypercube machine

G. V. S. Raju, Yi-chang Xu, Rodney M. Larson, Hatem N. Nasr
1992 Model-Based Vision Development and Tools  
A notable characteristic of hypercube configuration is that many topologies such as ring, mesh, tree, and hypercube topologies can be embedded on the hypercube configuration.  ...  FigFig 3. 3 3 of hypercube structure for matching different topologies gives us great convenience when we are Ring topology embedded on a 3-dimensional cube handling various problems.  ... 
doi:10.1117/12.57115 fatcat:jcc2bovk7ngqfmbjmblmombg7m

Extended Fibonacci Cubes

Jie Wu
1997 IEEE Transactions on Parallel and Distributed Systems  
a much sparser network than the hypercube.  ...  The EFC k s can be considered as flexible versions of incomplete hypercubes, which eliminates their restriction on the number of nodes, and, thus, makes it possible to construct parallel machines with  ...  When a network is embedded in a (regular or Extended) Fibonacci Cube, the quality of embeddings can be measured by the ratio of the size of the embedded network to the size of the embedding cube (which  ... 
doi:10.1109/71.640012 fatcat:eaamgtxydvgfpoqctb2x2z3uui

Page 5120 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
In this paper, we address the unsolved issue of embedding trees and grids in in- complete hypercubes.  ...  in incomplete hypercubes.  ... 
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