Mounir Hamdi, S. W. Song · IEEE Transactions on Parallel and Distributed Systems · 1997
The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings, the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes a new embedding method, based on matrix transformations, for optimally embedding hierarchical hypercube networks (HHNs) into the hypercube (binary n-cube). Thus, this embedding method has practical importance in enhancing the capabilities and extending the usefulness of the hypercube, since hierarchical hypercube networks have proven to be very cost-effective for a wide range of applications.
Cited by 12
Xiao Li, Jinwei Cao, Jun‐Ming Xu · arXiv (Cornell University) · 2012
The varietal hypercube $VQ_n$ is a variant of the hypercube $Q_n$ and has better properties than $Q_n$ with the same number of edges and vertices. This paper proves that $VQ_n$ is vertex-transitive. This property shows that when $VQ_n$ is used to model an interconnection network, it is high symmetrical and obviously superior to other variants of the hypercube such as the crossed cube.
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Chang Liu · 1999
Hypercube is one of the most commonly used topological structures for distributed memory systems. There have been a number of fault tolerant routing algorithm proposed in previous work. While, none of these previous schemes can work when there are more than 2 n -2 processors failed in a system of multiprocessors connected with n dimensional hypercube network. In this paper, this problem is deeply studied.Let H n be a n dimensional Hypercube network with fault node set F,|F|4n-24,(n10),(s 0,d 0) and ( s 1,d 1 ) be two pairs of nodes in H n-F . If they satisfy, (1) |A(v, H n-F)|6 for arbitrary v∈V(H n) .(2) H n can be parted into two subgraphs, ( d 0∈)H n-1,0 and (d 1∈)H n-1,1 , and |F∩H n-1,i |2n-12, for i=0,1. Then,there are two disjoint fault free paths P(s i,d i) ,such that, |P(s i,d i)|H(s i,d i)+12,(i=0,1), and the two paths can be parallel constructed.The corresponding fault tolerant routing algorithm which its time complexity is t=O(n· |F|) is given in this paper.
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S. Q. Zheng, S. Latifi, E. K. Park · 1993
Article Free Access Share on Sparse hypercube-like interconnection networks Authors: S. Q. Zheng View Profile , S. Latifi View Profile , E. K. Park View Profile Authors Info & Claims SAC '93: Proceedings of the 1993 ACM/SIGAPP symposium on Applied computing: states of the art and practiceMarch 1993 Pages 694–700https://doi.org/10.1145/162754.167182Online:01 March 1993Publication History 0citation171DownloadsMetricsTotal Citations0Total Downloads171Last 12 Months1Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF
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Tarun Tomar, S.C. Gupta, Prof S. C. Gupta · 2001
this paper we describe fault tolereant method in hyper-cube network. In this method we will consider that the faults are distributed in whole network. We also to drive the relation for the path length with the fault variation. In this paper we study the effect of link faults on the the path length for a faulty hpercube network such that the number of faulty links per node are less than n/2. we also suggest a model for simulation and measuring the performance of the system
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NTUR (臺灣機構典藏) · 2007
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S. Saffren, D. Angel · 2022 Third International Conference on Intelligent Computing Instrumentation and Control Technologies (ICICICT) · 2022
Tracing cells and electrons in network graphs which is often used in chemical industries, life science branches, cybersecurity and so on. It will be more applicable if the acyclic matching is determined for such graphs. Finding the maximum cardinality of acyclic matching is the acyclic matching problem, this can be calculated by observing the nature of graph network for n ≥ 1. Obtaining acyclic matching number for hypercubes is beneficial since it plays a major role in electronic and wireless communication areas and to precise the acyclic matching number, comparison between acyclic matching and perfect matching would be more helpful.
Cited by 4
Albert Greenberg, Bruce Hajek · IEEE Transactions on Communications · 1992
An approximate analysis of the transient and steady state behavior of deflection routing in hypercube networks is presented, under a uniform traffic model. In deflection routing congestion causes packets admitted to the network to be temporarily misrouted rather than buffered or dropped. The approximations show that deflection routing performs remarkably well in hypercube networks, for small as well as large networks and for the whole range from light to heavy load. Simulations suggest that the approximations are quite accurate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 114
Marie-Claude Heydemann, Joseph G. Peters, Dominique Sotteau · SIAM Journal on Discrete Mathematics · 1996
A spanning subgraph $G'$ of a simple undirected graph G is a t-spanner of G if every pair of vertices that are adjacent in G are at distance at most t in $G'$. The parameter t is called the dilation of the spanner. Spanners with small dilations have many applications, such as their use as low-cost approximations of communication networks with only small degradations in performance. In this paper, we derive spanners with small dilations for four closely related bounded-degree approximations of hypercubes: butterflies, cube-connected cycles, binary de Bruijn graphs, and shuffle-exchange graphs. We give both direct constructions and methods for deriving spanners for one class of graphs from spanners for another class. We prove that most of our spanners are minimum in the sense that spanners with fewer edges have larger dilations.
Cited by 21
Hyeong-seok Lim, Pancyclicity Of, Jung-heum Park et al. · 2016
Abstract. In this paper, we deal with the graph G0⊕G1 obtained from merging two graphs G0 and G1 with n vertices each by n pairwise non-adjacent edges joining vertices in G0 and vertices in G1. The main prob-lems studied are how fault-panconnectivity and fault-pancyclicity of G0 andG1 are translated into fault-panconnectivity and fault-pancyclicity of G0⊕G1, respectively. Many interconnection networks such as hypercube-like interconnection networks can be represented in the form of G0 ⊕G1 connecting two lower dimensional networks G0 and G1. Applying our results to a class of hypercube-like interconnection networks called re-stricted HL-graphs, we show that in a restricted HL-graph G of degree m( ≥ 3), each pair of vertices are joined by a path in G\\F of every length from 2m − 3 to |V (G\\F) | − 1 for any set F of faulty elements (vertices and/or edges) with |F | ≤ m − 3, and there exists a cycle of every length from 4 to |V (G\\F) | for any fault set F with |F | ≤ m − 2.
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2015
W e introduce a class of graphs which are variants of t h e hypercube graph. M a n y of the properties of this class of graphs are s imilar t o tha t of the hypercube hence, we refer t o t h e m as t h e class of Hypercube-Like ( H L) graphs/networks. W e show that the hypercube, t h e twisted n-cube [l] and the multiply-twisted cube [2] are members of this class of graphs. W e also propose s im-ple strategies f o r distributed m u t i n g and broadcast and discuss s o m e issues regarding embedding other graphs and reconfiguration in such networks. 1
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Mahmoud Omari · 2000
This research focuses on developing optimal pointto-point routing algorithm for quad Tree-Hypercube networks (TITs). TH's have been introducad as new fixed interconnection networks. It was shown that they have many hypercube features such as self-routing. In addition, they have advantages over hypercubes in extendibility, diameter, and average distant. In this research, an optimal point-to-point routing algorithm will be presented for quad TITs. It will be shown that the time for routing messages between any two nodes in the network is in the order of 2k, where 2k is the diameter of the network. In addition, the parallel path property in quad Tree-Hypercubes will be studied and the number ofparaUei shortest paths will be computed.
Cited by 4Open access
Ma, Yiu Ming Sammy · Summit (Simon Fraser University) · 1995
The hypercube is one of the most popular interconnection networks.Not only does it have good topological structure but also nice symmetric properties.However, it has a major drawback that the degree is not bounded as the dimension increases.Because of this, some networks with bounded degree have been derived from the hypercube.Two of the most popular are butterfly graphs and cube-connected-cycles.They both inherit some properties from the hypercube.This thesis investigates these two networks.
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Shu-Li Zhao, Rong‐Xia Hao · IEEE Access · 2019
The g-good neighbor connectivity κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (G) and g-good-neighbor diagnosability t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G. So far, almost all known results about κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (G) and t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (G) are about special g except the hypercubes, the star graphs, the k-ary n-cubes, and so on. In this paper, we focus on κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) and t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) for the n-dimensional hierarchical hypercube network HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> for 1 ≤ g ≤ m - 1 and m ≥ 2, where n = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + m. We show that κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (m + 1 - g) for 1 ≤ g ≤ m - 1. In addition, we show that t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (m + 2 - g) - 1 under the PMC model and MM* model for 1 ≤ g ≤ m - 1.
Cited by 9Open access
M. A. Jafarizadeh, F. Eghbalifam, S. Nami · arXiv (Cornell University) · 2014
We investigate the hypercube networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and entanglement entropy between two special parts of Hypercube network, can be calculated. To this aim, first we use the stratification method to rewrite the adjacency matrix of the network in the stratification basis which is the matrix representation of the angular momentum. Then the entanglement entropy and Schmidt number for special partitions are calculated an- alytically by using the generalized Schur complement method. Also, we calculate the entanglement entropy between two arbitrary equal subsets (two equal subsets have the same number of vertices) in H(3, 2) and H(4, 2) numerically, and we give the minimum and maximum values of entanglement entropy in these two Hypercube network. Then we can conjecture the minimum and maximum values of entanglement entropy for equal subsets in H(d, 2).
Cited by 2Open access
Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 1994
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Abdelghani Bellaachia, A. Youssef · 2002
The banyan-hypercube (BH) is one of the recently introduced hypercube-based interconnection networks. Due to the importance of communication in the overall system performance in a multiprocessing environment, this paper presents a near-optimal personalized broadcasting algorithm on the BHs. The analysis of this algorithm for both BHs and hypercubes is conducted for both single-port communication and multiple-port communication. We show that personalized broadcasting for both networks have the same communication time in the single-port mode. In multiple-port mode, the performance of the BH depends on its number of levels. When the number of levels is less than 4, the BHs outperform the hypercubes. However, the hypercubes have better performance than the BHs with large number of levels (>4). When the number of levels is equal to 4, both networks have the same performance.
Cited by 1
S. Latifi, A. El-Amawy · 2003
A hypercube-based network with high reliability and fault-tolerance capabilities is proposed and analyzed. The network is constructed by adding some redundant links to the structure of the standard hypercube. It is shown that communication link reliability and path reliability in the new network are substantially better than those of the standard hypercube. This improvement is obtained only at the expense of an asymptotically zero overhead.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 1
Abdelghani Bellaachia, A. Youssef · 2002
Partitioning strategies, as well as data structures for partitioning, are proposed and studied. Simulation results of internal, external, and total fragmentations for uniform and exponential distributions of request sizes are presented and discussed. The buddy system strategy of partitioning the hypercube is also simulated for comparison purposes. It is shown that the banyan-hypercube (BH) exhibits a better internal fragmentation than the hypercube, and for large request sizes the total fragmentation of the two networks is comparable. It is also shown that the internal fragmentation in BH decreases as the number of levels of BH increases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 4
Wolfe, William, Wolfe, William · CSUN ScholarWorks (California State University, Northridge) · 2007
In this paper we review the spectral properties of the hypercube graph Q n and derive the Walsh functions as eigenvectors of the adjacency matrix.We then interpret the Walsh functions as states of the hypercube, with vertices labeled +1 and -1, and elucidate the regularity of the induced vertex neighborhoods and subcubes.We characterize the neighborhoods of each vertex in terms of the number of similar (same sign) and dissimilar (opposite sign) neighbors and relate that to the eigenvalue of the Walsh state.We then interpret the Walsh states as states of the inhibitory hypercube network, a neural network created by placing a neuron at each corner of the hypercube and -1 connection strength on each edge.The Walsh states with positive, zero, and negative eigenvalues are shown to be unstable, weakly stable, and strongly stable states, respectively.
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