scholarly journals Path Embeddings with Prescribed Edge in the Balanced Hypercube Network

Symmetry ◽  
2017 ◽  
Vol 9 (6) ◽  
pp. 79 ◽  
Author(s):  
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...  
Keyword(s):  
Balanced Hypercube ◽  
Hypercube Network

The genus of the balanced hypercube

2016 ◽  
Vol 08 (01) ◽  
pp. 1650008 ◽  
Author(s):  
Cairen Wenmao ◽  
Rong-Xia Hao ◽  
Weili He
Keyword(s):  
Balanced Hypercube ◽  
Hypercube Network

The balanced hypercube [Formula: see text] is a variant of the hypercube network [Formula: see text]. [Formula: see text] is superior to [Formula: see text] because [Formula: see text] has better properties with the same number of links and processors as well as a smaller diameter. In this paper, we prove that the genus of [Formula: see text] is [Formula: see text].

AREA EFFICIENT LAYOUT OF BALANCED HYPERCUBES

1995 ◽  
Vol 06 (04) ◽  
pp. 631-645 ◽  
Author(s):  
KE HUANG ◽  
JIE WU
Keyword(s):  
Efficient System ◽  
Strong Connectivity ◽  
Wafer Scale ◽  
System Reconfiguration ◽  
Faulty Processor ◽  
Balanced Hypercube ◽  
Wafer Scale Integration ◽  
Scale Integration ◽  
Area Efficient ◽  
Load Balanced

As a multicomputer structure, the balanced hypercube is a variant of the standard hypercube for multicomputers, with desirable properties of strong connectivity, regularity, and symmetry. This structure is a special type of load balanced graph designed to tolerate processor failure. In balanced hypercubes, each processor has a backup (matching) processor that shares the same set of neighboring nodes. Therefore, tasks that run on a faulty processor can be reactivated in the backup processor to provide efficient system reconfiguration. In this paper, we study the implementation of balanced hypercubes in VLSI using the Wafer Scale Integration (VLSI/WSI) technology. Emphasis is on VLSI/WSI layout and area estimates. Our results show that the balanced hypercube can be implemented at least as efficient as the standard hypercube in an area layout and more efficient in a linear layout.

Performance Evaluation, Comparison and Identification of Efficient Hypercube Interconnection Networks

2021 ◽  
Author(s):  
Karthik K ◽  
Sudarson Jena ◽  
Venu Gopal T
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Research Work ◽  
Processing Unit ◽  
Network Cost ◽  
Multi Stage ◽  
Memory Modules ◽  
Effective Performance ◽  
Twisted Cube ◽  
Hypercube Network

Abstract A Multiprocessor is a system with at least two processing units sharing access to memory. The principle goal of utilizing a multiprocessor is to process the undertakings all the while and support the system’s performance. An Interconnection Network interfaces the various handling units and enormously impacts the exhibition of the whole framework. Interconnection Networks, also known as Multi-stage Interconnection Networks, are node-to-node links in which each node may be a single processor or a group of processors. These links transfer information from one processor to the next or from the processor to the memory, allowing the task to be isolated and measured equally. Hypercube systems are a kind of system geography used to interconnect various processors with memory modules and precisely course the information. Hypercube systems comprise of 2n nodes. Any Hypercube can be thought of as a graph with nodes and edges, where a node represents a processing unit and an edge represents a connection between the processors to transmit. Degree, Speed, Node coverage, Connectivity, Diameter, Reliability, Packet loss, Network cost, and so on are some of the different system scales that can be used to measure the performance of Interconnection Networks. A portion of the variations of Hypercube Interconnection Networks include Hypercube Network, Folded Hypercube Network, Multiple Reduced Hypercube Network, Multiply Twisted Cube, Recursive Circulant, Exchanged Crossed Cube Network, Half Hypercube Network, and so forth. This work assesses the performing capability of different variations of Hypercube Interconnection Networks. A group of properties is recognized and a weight metric is structured utilizing the distinguished properties to assess the performance exhibition. Utilizing this weight metric, the performance of considered variations of Hypercube Interconnection Networks is evaluated and summed up to recognize the effective variant. A compact survey of a portion of the variations of Hypercube systems, geographies, execution measurements, and assessment of the presentation are examined in this paper. Degree and Diameter are considered to ascertain the Network cost. On the off chance that Network Cost is considered as the measurement to assess the exhibition, Multiple Reduced Hypercube stands ideal with its lower cost. Notwithstanding it, on the off chance that we think about some other properties/ scales/metrics to assess the performance, any variant other than MRH may show considerably more ideal execution. The considered properties probably won't be ideally adequate to assess the effective performance of Hypercube variations in all respects. On the off chance that a sensibly decent number of properties are utilized to assess the presentation, a proficient variation of Hypercube Interconnection Network can be distinguished for a wide scope of uses. This is the inspiration to do this research work.

Adaptive Wormhole Routing in Mesh-Hypercube Network

2004 ◽  
Vol 4 (4) ◽  
pp. 568-574 ◽  
Author(s):  
Bassam Al-Mahadeen . ◽  
Mahmoud Omari .
Keyword(s):  
Wormhole Routing ◽  
Hypercube Network

Edge Fault-Tolerant Strong Hamiltonian Laceability of Balanced Hypercubes

2016 ◽  
Vol 16 (02) ◽  
pp. 1650002 ◽  
Author(s):  
MEI-MEI GU ◽  
RONG-XIA HAO ◽  
YAN-QUAN FENG
Keyword(s):  
Bipartite Graph ◽  
Fault Tolerant ◽  
Hamiltonian Path ◽  
Balanced Hypercube ◽  
Hamiltonian Laceability

The balanced hypercube BHn, proposed by Wu and Huang, is a new variation of hypercube. A Hamiltonian bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path between two arbitrary vertices from different partite sets. A Hamiltonian laceable graph G is strongly Hamiltonian laceable if there is a path of length [Formula: see text] between any two distinct vertices of the same partite set. A graph G is called k-edge-fault strong Hamiltonian laceable, if G – F is strong Hamiltonian laceable for any edge-fault set F with [Formula: see text]. It has been proved that the balanced hypercube BHn is strong Hamiltonian laceable. In this paper, we improve the above result and prove that BHn is (n – 1)-edge-fault strong Hamiltonian laceable.

Communication Performance Evaluation of the Locally Twisted Cube

2020 ◽  
Vol 31 (02) ◽  
pp. 233-252
Author(s):  
Yuejuan Han ◽  
Lantao You ◽  
Cheng-Kuan Lin ◽  
Jianxi Fan
Keyword(s):  
Performance Evaluation ◽  
Interconnection Networks ◽  
High Performance ◽  
Communication Performance ◽  
Wide Diameter ◽  
Fault Diameter ◽  
Twisted Cube ◽  
Hypercube Network ◽  
High Performance Computers ◽  
Important Variant

The topology properties of multi-processors interconnection networks are important to the performance of high performance computers. The hypercube network [Formula: see text] has been proved to be one of the most popular interconnection networks. The [Formula: see text]-dimensional locally twisted cube [Formula: see text] is an important variant of [Formula: see text]. Fault diameter and wide diameter are two communication performance evaluation parameters of a network. Let [Formula: see text]), [Formula: see text] and [Formula: see text] denote the diameter, the [Formula: see text] fault diameter and the wide diameter of [Formula: see text], respectively. In this paper, we prove that [Formula: see text] if [Formula: see text] is an odd integer with [Formula: see text], [Formula: see text] if [Formula: see text] is an even integer with [Formula: see text].

Structure Fault Tolerance of Recursive Interconnection Networks

2020 ◽  
Author(s):  
Eminjan Sabir ◽  
Jixiang Meng
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Theoretical Problem ◽  
Connected Subgraph ◽  
Edge Connectivity ◽  
Minimum Cardinality ◽  
Edge Disjoint ◽  
Balanced Hypercube

Abstract Motivated by effects caused by structure link faults in networks, we study the following graph theoretical problem. Let $T$ be a connected subgraph of a graph $G$ except for $K_{1}$. The $T$-structure edge-connectivity $\lambda (G;T)$ (resp. $T$-substructure edge-connectivity $\lambda ^s(G;T)$) of $G$ is the minimum cardinality of a set of edge-disjoint subgraphs $\mathcal{F}=\{T_{1},T_{2},\ldots ,T_{m}\}$ (resp. $\mathcal{F}=\{T_{1}^{^{\prime}},T_{2}^{^{\prime}},\ldots ,T_{m}^{^{\prime}}\}$) such that $T_{i}$ is isomorphic to $T$ (resp. $T_{i}^{^{\prime}}$ is a connected subgraph of $T$) for every $1 \le i \le m$, and $E(\mathcal{F})$’s removal leaves the remaining graph disconnected. In this paper, we determine both $\lambda (G;T)$ and $\lambda ^{s}(G;T)$ for $(1)$ the hypercube $Q_{n}$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},P_{4},Q_{1},Q_{2},Q_{3}\}$; $(2)$ the $k$-ary $n$-cube $Q^{k}_{n}$$(k\ge 3)$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},Q^{3}_{1},Q^{4}_{1}\}$; $(3)$ the balanced hypercube $BH_{n}$ and $T\in \{K_{1,1},K_{1,2},BH_{1}\}$. We also extend some known results.

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