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

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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