### 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 language | English |
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Title of host publication | Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04 |

Editors | H.R. Arabnia, J. Ni |

Pages | 738-743 |

Number of pages | 6 |

Volume | 2 |

Publication status | Published - 2004 |

Externally published | Yes |

Event | Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04 - Las Vegas, NV Duration: 21 Jun 2004 → 24 Jun 2004 |

### Other

Other | Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04 |
---|---|

City | Las Vegas, NV |

Period | 21/6/04 → 24/6/04 |

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - On hierarchical extensions of large-scale 4-regular grid network structures

AU - Pedersen, Jens Myrup

AU - Patel, Ahmed

AU - Knudsen, Thomas Phillip

AU - Madsen, Ole Brun

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Large-Scale Networks

KW - Network Planning

KW - Network Structures

KW - Routing

KW - Topological Routing

UR - http://www.scopus.com/inward/record.url?scp=12344335902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12344335902&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:12344335902

SN - 1932415262

SN - 9781932415261

VL - 2

SP - 738

EP - 743

BT - Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'04

A2 - Arabnia, H.R.

A2 - Ni, J.

ER -