Generating Realistic Network Topologies for Simulation Purposes

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Generating Realistic Network Topologies for
Simulation Purposes

• Junhong Sun and Michalis Faloutsos
• Department of Computer Science
• University of California, Riverside
• junhong, michalis_at_cs.ucr.edu

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Motivation

• Most network simulations are computationally
  intensive.
• Needs small and realistic topology models.
• Real Internet topology instances are huge.
• Most topology generators cant create realistic
  topologies, and the synthesized graphs exhibit
  the absence of some important topological
  properties.

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Our Approach

• We start from a large real topology, and reduce
  it repeatedly until it reaches the desired size.
• A set of topological metrics is used to validate
  the realism of the reduced graphs.
• We propose two algorithms
• Iterative Reduction Algorithm uses a
  user-specified method to reduce a graph
  repeatedly.
• Combined Reduction Algorithm combines different
  methods to achieve enhanced performance.

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Topological Metrics

• Average out-degree
• Out-degree distribution
• C1 degree ?28 C2 degree 10-27
• C3 degree 4-9 C4 degree 1-3
• Power-Law 1
• out-degree vs. rank
• Power-Law 2
• number of nodes vs. out-degree
• Theyre invariant over time and we use them to
  validate the realism of the reduced graphs.

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Graph Reduction Methods

• Removal of nodes or edges
• Random Vertex Deletion (RVD)
• Random Edge Deletion (RED)
• Merging/Clustering of nodes
• Edge Shrinking (SRK) shrinks an edge into a node
• Clustering (CLST) merges neighbors of u and u
  itself into one node
• Induced subgraphs
• Subgraph by BFS (BFS) extracts a subgraph by BFS
• Subgraph by DFS (DFS) extracts a subgraph by DFS

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Iterative Reduction Algorithm
STOP
Yes
No
Measure topological metrics of the reduced graph
Reduce a small percent of G using method M
Real topology G
Choose a method M
Desired Size
Method Pool
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Our Approach Works

• Performance consistence
• Running 50 times with different random seeds
• Running on multiple instances of different sizes
• 67 of the original graph is removed, and 3 is
  deleted in each iteration.
• All methods show consistent performance.
• Random Edge Deletion shows the best performance
• Clustering performs less satisfactorily
• Topological properties are approximately kept.

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Power-Laws are Preserved

• In most cases, power-law properties are preserved
  during the reduction process

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We Can Still Improve It

• Repeatedly applying the same method on the graph
  works.
• Out-degree distribution and power-laws are
  invariant, but our methods change them slightly.
• We have a diversified method pool. It is possible
  to generate better results by combining them
• Selects a different method to correct the
  negative effects brought by methods in the
  previous iterations.

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Combined Reduction Algorithm
Real topology G
Randomly choose an initial method M
Desired Size
Method Pool
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How to Choose a Method?

• Metric target models are extracted from
  variations of those metrics of the real Internet
  topology.
• slope represents the effect of a method on this
  metric.

• The method that has the smallest overall
  predicted deviation is selected for the next
  iteration.

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Combined Algorithm is Better
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Discussion

• We compare the combined algorithm and the
  iterative algorithm using RED.
• The combined algorithm shows the capability to
  correct metric deviations during the reduction
  process.
• The generated small graphs have the desired
  topological properties.
• When a large percentage of the original graph is
  removed, the combined algorithm shows better
  performance.

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The Significance of Our Approach

• We follow the opposite direction from commonly
  used graph generators.
• By reducing from large real topology, we can
  generate small graphs with desired topological
  properties.
• Our approach could potentially preserve some
  unknown properties of the Internet.
• The small graphs generated by our approach are
  considered more realistic.

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Future Works

• To validate the realism and usefulness of our
  algorithms by running various simulations on both
  the original topology and on our generated small
  graphs.
• To incorporate some application-specific metrics
  to generate graphs for intended use.