Embedding star networks into hypercubes

“…Star graph class is mostly based on how to generate a node in star graph and has difference in how to generate an edge. Star graph class includes hyperstar HS(m,k) [6], star-crossed cube SCQ(m,n) [7], folded hyper-star FHS(2n,n) [8], hierarchical star HS(n,n) [9], macro star MS(m,n) [10], transposition graph [11], matrix star [12], pancake graph [13], and half pancake graph [15].…”

Section: Introductionmentioning

confidence: 99%

Embedding Algorithm among Half Pancake, Pancake, and Star Graphs

Seo

Lee

2016

IJSEIA

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The star graph is an attractive alternative to hypercube. The pancake graph has n! nodes and generates edge using exchange of a symbol that composes a node address like star graph. The half pancake graph is a new network where the network cost of pancake graph is reduced by half. We suggest embedding algorithm among these networks. The half pancake HP n was embedded on pancake P n with dilation 1 and congestion 1. The half pancake P n was embedded on star graph S n with dilation 1.5n-2, average dilation about 0.25n+4, and congestion 6. The pancake P n was embedded on star graph S n with dilation 1.5n. All the three of embedding were one-to-one embedding with expansion 1.

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“…For nodes and edges composing the interconnection networks, the algorithm developed in G is reusable in the algorithm H by matching the node of G with that of H and the edge of G with the path of H. Given a guest graph G and a host graph H, embedding of G in H is described by an ordered pair (Φ, Ψ), where Φ maps each node of G to a node of H and Ψ maps each edge (u, v) of G to a path of H from nodes Φ(u) to Φ(v) (hereafter referred to as Ψ-path). Dilation of the edge (u, v) is the length of the Ψ-path in H, and dilation of the embedding (Φ, Ψ) is the largest value among dilations for all edges of G. Congestion of the edge of H is Ψ-paths traversing an edge of H, and congestion of the embedding (Φ, Ψ) is the largest value among congestions for all edges of H. Expansion of the embedding (Φ, Ψ) is a ratio of the number of nodes of G to that of H [ 16 , 17 ]. The measures to evaluate the embedding algorithm are dilation, congestion, and expansion.…”

Section: Introductionmentioning

confidence: 99%

“…Studies on embedding between interconnection networks include embedding tree, cycle, mesh, hypercube, and star graph into other interconnection networks [ 17 – 20 ], and embedding among mesh, hypercube, and star graph [ 21 , 22 ]. In a study on embedding among mesh classes, the embedding measures are mostly one place integers.…”

Section: Introductionmentioning

confidence: 99%

One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks

Seo

Sim

Park

et al. 2011

Sensors

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As wireless mobile telecommunication bases organize their structure using a honeycomb-mesh algorithm, there are many studies about parallel processing algorithms like the honeycomb mesh in Wireless Sensor Networks. This paper aims to study the Peterson-Torus graph algorithm in regard to the continuity with honeycomb-mesh algorithm in order to apply the algorithm to sensor networks. Once a new interconnection network is designed, parallel algorithms are developed with huge research costs to use such networks. If the old network is embedded in a newly designed network, a developed algorithm in the old network is reusable in a newly designed network. Petersen-Torus has been designed recently, and the honeycomb mesh has already been designed as a well-known interconnection network. In this paper, we propose a one-to-one embedding algorithm for the honeycomb mesh (HMn) in the Petersen-Torus PT(n,n), and prove that dilation of the algorithm is 5, congestion is 2, and expansion is 5/3. The proposed one-to-one embedding is applied so that processor throughput can be minimized when the honeycomb mesh algorithm runs in the Petersen-Torus.

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Embedding star networks into hypercubes

Cited by 16 publications

References 22 publications

Embedding of cycles and wheels into arbitrary trees

Embedding of cycles and wheels into arbitrary trees

Embedding Algorithm among Half Pancake, Pancake, and Star Graphs

One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks

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