A criterion for cost optimal construction of irregular networks
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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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A criterion for cost optimal construction of irregular networks

A Criterion forCost Optimal Construction ofIrregular Networks

Geir Horn, Olav Lysne and Tor Skeie


Classical question

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)


Our reverse question

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)


Our question today

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)


Assumptions

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)


The switch size

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)


The number of switches

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)


Combined optimum

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)


The solution

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


Example topology

Example Topology

Complete

Part

3

5

1

4

2

6

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


Topological properties

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


Simulated topologies

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%


Domain of applicability

Domain of Applicability

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


Conclusions further work

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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