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A Criterion for Cost Optimal Construction of Irregular Networks

A Criterion for Cost Optimal Construction of Irregular Networks. Geir Horn, Olav Lysne and Tor Skeie. Classical Question. Given a set of switches, and a set of nodes what is the best performance you can get when connecting these components?. Our Reverse Question.

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A Criterion for Cost Optimal Construction of Irregular Networks

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  1. A Criterion forCost Optimal Construction ofIrregular Networks Geir Horn, Olav Lysne and Tor Skeie

  2. Classical Question Given a set of switches, and a set of nodes what is the best performance you can get when connecting these components? G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  3. Our Reverse Question Given a set of nodeshow should the networkand its switches be constructed to best support these nodes? G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  4. Our Question Today Given the need to connect a set of nodes, and a traffic pattern: • What is the least number of switches necessary? • What is the minimal size of each switch necessary? • What topology should be used? G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  5. Assumptions • Uniform traffic distribution • Uniform distribution of nodes over the switches • No parallel links G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  6. The Switch Size Number of nodes hosted Number of links to the network Intuitively: G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  7. The Number of Switches Maximum number of links to the network on any switch G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  8. Combined Optimum Minimise the maximal switch degree • Smallest possible switches • Least number of switches G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  9. The Solution • Size of biggest switch, • Number of links on each switch to the network Algorithmic mapping • Input: • Even number of nodes, • Output: • Number of switches, G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03) It is always possible to construct a networkwith these switches

  10. Example Topology Complete Part 3 5 1 4 2 6 G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  11. Topological Properties • Complete graphs (networks) whenever • Exponentially growing number of isomorphic classes for network sizes immediately following a complete network • Example: is complete, and has 22 isomorphic classes G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03) • Always a complete part of the network • Maximum shortest path is of length two

  12. Simulated Topologies 1 2 3 G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03) 5 7 4 6 Complete part Saturation point = 63.5% Saturation point = 63.5% Saturation point = 57.2% 63.5% 63.5% 57.2%

  13. Domain of Applicability G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03)

  14. Conclusions & Further work • Work-in-progress report • Optimality = Simultaneously minimise • The number of switches • The size of the switches • Algorithmic solution G. Horn et al: Cost Optimal Construction of Irregular Networks (CAC'03) • Further work: • Solutions for fixed size switches? • How to select the best performing network? • Scalability for clustered traffic?

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