Linear Wirelength of Folded Hypercubes

Rajasingh, Indra; Arockiaraj, Micheal

doi:10.1007/s11786-011-0085-2

Cited by 29 publications

(6 citation statements)

References 11 publications

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“…Proof. In [32] it was proved that BW (F Q n ) = 2 n , and with Theorem 3 this implies W L(F Q n , Q n ) n2 n . To prove the reverse inequality, let id : F Q n → Q n be the identity embedding, that is, id(v) = v, for every v ∈ V (F Q n ) (and where the second v is considered as a vertex of Q n ).…”

Section: Embeddings Of Folded Hypercubesmentioning

confidence: 92%

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

et al. 2020

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Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is the hypercube due to its structural regularity, potential for parallel computation of various algorithms, and the high degree of fault tolerance. Thus it becomes the first choice of topological structure of parallel processing and computing systems. In this paper, lower bounds for the dilation, wirelength, and edge congestion of an embedding of a graph into a hypercube are proved. Two of these bounds are expressed in terms of the bisection width. Applying these results, the dilation and wirelength of embedding of certain complete multipartite graphs, folded hypercubes, wheels, and specific Cartesian products are computed.

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Section: Embeddings Of Folded Hypercubesmentioning

confidence: 92%

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

et al. 2020

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“…The second embedding scheme is the lex embedding widely used in many works. 13,20,39 By lex embedding what we mean is that, the guest graph attains maximum subgraph when the vertices are ordered lexicographically. The last embedding scheme is the random embedding 33 denoted by rand, where the random bijection rand ∶ V(G) → V(H), with the condition that rand ≠ 𝜙 or lex.…”

Section: Simulation Experimentsmentioning

confidence: 99%

Optimization of layout for embedding half hypercube into conventional tree architectures

Immanuel,

Greeni

2024

Concurrency and Computation

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SummaryEmbedding a graph into another graph can be utilized for structural simulation, processor allocation, and algorithm porting in the field of parallel architecture. This has the potential to enhance the physical layout of network‐on‐chip (NoC) devices as well as to investigate their virtualization possibilities. Layout is one of the many indicators of graph embedding. An optimal layout in NoC design can result in a decreased wiring area and cost, as well as the reduction in communication delay between parallel processing components. In this work, the guest graph is the half hypercube, which possess efficient routing, fault tolerance, and Hamiltonian features. The edge isoperimetric problems is solved for the half hypercube using a novel technique called the isochronal ordering. The host graphs considered in our work are complete binary trees, ‐rooted complete binary trees, and other few predominantly investigated tree based architectures.

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“…4. We need the following results [20,21] pertaining to folded hypercube for our further study. Theorem 4:…”

Section: Linear Ordering Of Enhanced Hypercubesmentioning

confidence: 99%

Vertex decomposition method for wirelength problem and its applications to enhanced hypercube networks

Arockiaraj¹,

Liu

Shalini³

2018

IET Computers & Digital Techniques

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In this study, the authors discuss the vertex congestion of any embedding from the guest graph into the host graph and outline a rigorous mathematical method to compute the wirelength of that embedding. Further, they show that the computation of the optimal wirelength depends on finding optimal solutions for another graph partition problem such as edge isoperimetric problem in that guest graph. On the other side, they consider an important variant of the popular hypercube network, the enhanced hypercube, and obtain the nested optimal solutions for the edge isoperimetric problem. As a combined output, they illustrate the authors' technique by embedding enhanced hypercube into a caterpillar and from that reducing the linear layout of the enhanced hypercube. As another application of their technique, they embed the hypercube as well as the enhanced hypercube on the two rows extended grid structure with optimal wirelength for the first time and showing that the existing edge congestion technique cannot be used to solve this problem.

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Linear Wirelength of Folded Hypercubes

Cited by 29 publications

References 11 publications

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

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

Optimization of layout for embedding half hypercube into conventional tree architectures

Vertex decomposition method for wirelength problem and its applications to enhanced hypercube networks

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