On hierarchical extensions of large-scale 4-regular grid network structures

Jens Myrup Pedersen, Ahmed Patel, Thomas Phillip Knudsen, Ole Brun Madsen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

It is studied how the introduction of ordered hierarchies in 4-regular grid network structures decreases distances remarkably, while at the same time allowing for simple topological routing schemes. Both meshes and tori are considered; In both cases non-hierarchical structures have power-law dependencies between the number of nodes and the distances in the structures. The perfect square mesh is introduced for hierarchies, and it is shown that applying ordered hierarchies in this way results in logarithmic dependencies between the number of nodes and the distances, resulting in better scaling structures. For example, in a mesh of 391876 nodes the average distance is reduced from 417.33 to 17.32 by adding hierarchical lines. This is gained by increasing the number of lines by 4.20% compared to the non-hierarchical structure. A similar hierarchical extension of the torus structure also results in logarithmic dependencies, the relative difference between performance of mesh and torus structures being less significant than for non-hierarchical structures, especially for large structures. The skew and extended meshes are introduced as variants of the perfect square mesh and their performances studied, and it is shown that while they allow for more flexibility in design and construction of structures supporting topological routing, their performances are comparable to the performance of the perfect square mesh. Finally suggestions for further research within the field is given.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04
EditorsH.R. Arabnia, J. Ni
Pages738-743
Number of pages6
Volume2
Publication statusPublished - 2004
Externally publishedYes
EventProceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04 - Las Vegas, NV
Duration: 21 Jun 200424 Jun 2004

Other

OtherProceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04
CityLas Vegas, NV
Period21/6/0424/6/04

Keywords

  • Large-Scale Networks
  • Network Planning
  • Network Structures
  • Routing
  • Topological Routing

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Pedersen, J. M., Patel, A., Knudsen, T. P., & Madsen, O. B. (2004). On hierarchical extensions of large-scale 4-regular grid network structures. In H. R. Arabnia, & J. Ni (Eds.), Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04 (Vol. 2, pp. 738-743)

On hierarchical extensions of large-scale 4-regular grid network structures. / Pedersen, Jens Myrup; Patel, Ahmed; Knudsen, Thomas Phillip; Madsen, Ole Brun.

Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04. ed. / H.R. Arabnia; J. Ni. Vol. 2 2004. p. 738-743.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pedersen, JM, Patel, A, Knudsen, TP & Madsen, OB 2004, On hierarchical extensions of large-scale 4-regular grid network structures. in HR Arabnia & J Ni (eds), Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04. vol. 2, pp. 738-743, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04, Las Vegas, NV, 21/6/04.
Pedersen JM, Patel A, Knudsen TP, Madsen OB. On hierarchical extensions of large-scale 4-regular grid network structures. In Arabnia HR, Ni J, editors, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04. Vol. 2. 2004. p. 738-743
Pedersen, Jens Myrup ; Patel, Ahmed ; Knudsen, Thomas Phillip ; Madsen, Ole Brun. / On hierarchical extensions of large-scale 4-regular grid network structures. Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04. editor / H.R. Arabnia ; J. Ni. Vol. 2 2004. pp. 738-743
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