Embedding algorithm of spined cube into grid structure and its wirelength computation

Arockiaraj, Micheal; Shalini, Arul Jeya; Delaila, J. Nancy

doi:10.1016/j.tcs.2021.12.016

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…With the advancement of modern science and technology, the development of industry and the needs of future human development, modern civil engineering structures are developing in the direction of large-scale, spatial, and complex. These large complex structures, such as bridges, dams, high-rise buildings, offshore structures, and large-span space grid structures, etc., after being put into use in a complex service environment, it is faced with the problem of structural damage accumulation under the influence of design load changes and various sudden external factors [ 1 ]. Therefore, if the damage to the structure cannot be found in time and effective measures are taken to deal with it, it will lead to structural damage; it can even lead to catastrophic consequences, causing threats or even losses to the life and property of the country and the people.…”

Section: Introductionmentioning

confidence: 99%

Application of Particle Swarm Algorithm in Nanoscale Damage Detection and Identification of Steel Structure

Zhang

2022

International Journal of Analytical Chemistry

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In order to identify the damage of a grid structure, the author proposes a damage identification method for grid structures based on particle swarm optimization. First, using the Modal Assurance Criterion (MAC) and combining the respective advantages of frequency and mode shape in damage identification, a fitness function based on frequency and mode shape is constructed. Second, two test functions are used to compare and analyze, which shows that the improved particle swarm algorithm has better optimization performance. Finally, through an example of a grid structure simulation model, the effectiveness of the proposed method is verified. Three working conditions were set up for damage identification, and the results were analyzed. Results. The particle swarm calculation of case 1 converged in the 53rd generation, and case 2 completed the convergence in the 67th generation, which is consistent with the actual situation. Condition 3 completed the convergence at the 125th generation, indicating that the fitness value has been decreasing until then, and it does not change after the convergence, indicating that the convergence is good. The damage degree of No. 92 member was identified as 95.69%, and the damage degree of No. 105 member was 96.28%. Basically, this is in line with the actual situation. Conclusions. The damage identification method based on the particle swarm algorithm can accurately identify the location and degree of damage.

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Section: Introductionmentioning

confidence: 99%

Application of Particle Swarm Algorithm in Nanoscale Damage Detection and Identification of Steel Structure

Zhang

2022

International Journal of Analytical Chemistry

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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%

“…Until then only approximations were given in the form of bounds 10,15,17 . Here are few works which are concerned about optimizing the layout for the considered embedding: complete Josephus cube into tree related architectures, 8 balanced complete multipartite graphs onto cartesian product between {Path, Cycle} and trees, 18 balanced complete multipartite graphs onto grids and tree related structures, 19 spined cube into grid, 20 complete bipartite graph into sibling tree, 21 augmented cube into tree related and windmill structures, 9 fault tolerance mapping of ternary

N

‐cube onto chips, 4 hierarchical cube into linear array and

k

‐rooted complete binary trees, 5 hierarchical folded cubes into linear arrays and complete binary trees, 1 circular layout of hypercube, 12 hypercube into certain trees, 6 locally twisted cube into grid, 13 familiar graphs onto hypercube, 7 hypercube into cylinder, 14 and 3‐Ary

n

‐cube into grid 22 …”

Section: Introductionmentioning

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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“…The computational cost of a parallel computing system is heavily dominated by the communication cost of the underlying network, which decides the overall performance of the system. This fact clearly emphasizes the significance of network topology and its efficient structural designs [6,30]. The topological structure of the underlying network can be modeled as a graph where vertices correspond to processors, memory modules or switches, and edges correspond to communication links.…”

Section: Introductionmentioning

confidence: 99%

“…The diameter of SQ n is only ⌈ n 3 ⌉ + 3, which is less than many known variants such as crossed cubes, twisted cubes, Möbius cubes, etc. The spined cube has attracted the attention of many researchers, and its various properties such as embedability [6], reliability [11], the shortest-path routing [28] have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Yang¹,

Zhang²,

Yan³

et al. 2022

Preprint

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The spined cube SQn is a variant of the hypercube Qn, introduced by Zhou et al. in [Information Processing Letters 111 (2011) 561-567] as an interconnection network for parallel computing. A graph Γ is an m-Cayley graph if its automorphism group Aut(Γ) has a semiregular subgroup acting on the vertex set with m orbits, and is a Caley graph if it is a 1-Cayley graph. It is well-known that Qn is a Cayley graph of an elementary abelian 2-group Z n 2 of order 2 n . In this paper, we prove that SQn is a 4-Cayley graph of Z n−2 2 when n ≥ 6, and is a ⌊n/2⌋-Cayley graph when n ≤ 5. This symmetric property shows that an n-dimensional spined cube with n ≥ 6 can be decomposed to eight vertex-disjoint (n − 3)-dimensional hypercubes, and as an application, it is proved that there exist two edge-disjoint Hamiltonian cycles in SQn when n ≥ 4. Moreover, we determine the vertex-transitivity of SQn, and prove that SQn is not vertex-transitive unless n ≤ 3.

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Embedding algorithm of spined cube into grid structure and its wirelength computation

Cited by 7 publications

References 24 publications

Application of Particle Swarm Algorithm in Nanoscale Damage Detection and Identification of Steel Structure

Application of Particle Swarm Algorithm in Nanoscale Damage Detection and Identification of Steel Structure

Optimization of layout for embedding half hypercube into conventional tree architectures

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

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