Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

Manuel, Paul; Arockiaraj, Micheal; Rajasingh, Indra; Rajan, Bharati

doi:10.1016/j.dam.2011.07.003

Cited by 37 publications

(18 citation statements)

References 37 publications

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“…Even in daily life it is used extensively in cellphones, digital cameras, MP3 players, portable digital assistants and automobile antilock brake systems, etc. Seeing its importance and its studies by various authors in the literature ([3], [8][9][10][11][12][13][14][15][16][17], [21]) we were motivated towards working out theoretically the embedding signed-regular graphs in higher order signed-regular graphs.…”

Section: Introductionmentioning

confidence: 99%

Embedding of signed regular graphs

Sinha¹,

Rao²

2018

NNTDM

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A signed graph is a graph whose edges carry the weight '+' or '−'. A signed graph S is called signed-regular if d − (v) is same for all v ∈ V and d + (v) is same for all v ∈ V. The problems of embedding (i, j)-signed-regular graphs in (i, j + l)-signed-regular graphs is one of the fascinating problems from application point of view, which is dealt in this paper with insertion of least number of vertices in S.

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Section: Introductionmentioning

confidence: 99%

Embedding of signed regular graphs

Sinha¹,

Rao²

2018

NNTDM

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“…Therefore, a minimum congestion is a most desirable feature in network embedding [3]. Congestion of an embedding has been well studied for a number of networks [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A Tight Bound for Congestion of an Embedding

Manuel

Rajasingh

Rajan

et al. 2015

Algorithms and Discrete Applied Mathematics

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Abstract. Graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. Congestion is one of the main optimization objectives in global routing. In this paper, we introduce a technique to obtain a tight bound for congestion of an embedding. Moreover, we give algorithms to compute exact congestion of embedding the hypercubes into the cylinder and the torus and prove that the bound obtained is sharp.

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“…But the Congestion Lemma and the Partition Lemma [24] have enabled to obtain exact wirelength of embeddings for various architectures [23][24][25]29,[31][32][33]. This technique focuses on specific partitioning of the edge set of the host graph.…”

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confidence: 98%