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 forCost Optimal Construction ofIrregular 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?

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

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

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
• Uniform traffic distribution
• Uniform distribution of nodes over the switches

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

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

Maximum number of links to the network on any switch

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

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
• 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

Complete

Part

3

5

1

4

2

6

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

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

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

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

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?