Mapping the Internet Topology
Via Multiple Agents
What does the internet look like?
Why do we care?
• While communication protocols will work
correctly on ANY topology
….they may not be efficient for some
topologies
• Knowledge of the topology can aid in
optimizing protocols
Topics
• Power laws in the internet topology
• Sampling bias in existing topology
measurements
• The DIMES project
• Potential applications
• Open issues
Mapping the Internet
• Required characteristics:
– connectivity
– delays
• Metrics
– In/Outdegree
– Distance (delay – problematic definition)
Problem definition
G – (un)directed graph
N – number of nodes
E – number of edges
dv – outdegree of a node v
fd – frequency of an outdegree
P(h) – number of pairs in the “h-hop
neighborhood”
On Power-law Relationships of the
Internet Topology
Oct. 1999, Faloutsos Bros.
Mapped the internet at the AS and router
level using BGP route views
Data sets:
– Nov. ’97: 3015 nodes, 5156 edges
– Apr. ’98: 3530 nodes, 6432 edges
– Dec. ’98: 4389 nodes, 8256 edges
Outdegree Exponent Power Law
fd ~ d^σ
Other places that people look
for power laws…
SCIENCE CITATION INDEX
Nodes: papers
Links: citations
25
Witten-Sander
PRL 1981
1736 PRL papers (1988)
2212
P(k) ~k-
( = 3)
(S. Redner, 1998)
Sex-web
Nodes: people (Females; Males)
Links: sexual relationships
4781 Swedes; 18-74;
59% response rate.
Liljeros et al. Nature 2001
Recall – the Faloutsos graph
Is It Really Power Law?
• Sampling bias could exist
• Crovella article title
• Target – find out if bias exists in prevailing
measurement methods, and identify the
sources for this bias.
• Configuration – graph model, sampling
method, distributions, why this is similar to
currently used methods
Results
• Erdos – Renyi + graphs
Sources of sampling bias
•
•
•
•
Disproportional sampling of nodes
Disproportional sampling of edges
Conclusion
Identify problems in existing measurement
methods (Faloutsos, Caida)
Analysis of Bias Cause
• Explanation
– Better coverage with more measurement
sources
DIMES
• Targets
• How we try to solve the problem
DIMES Platform
• Description
• Screenshot
Internet according to DIMES
• maps
Application
• Research
– Simulations
• Developing new algs, protocols
• Evolution (how will the internet look like in 2020?)
• Testing new tools, manufacturing scenarios
– “pure” research
• Studying the internet “behavior”, growth
• Developing models to describe it
More Application
• Potentially commercial
– Improve existing algs’ using knowledge about
the characteristics of the internet.
• Multicast alg’
• Low – priority packet routing
– Identify (and work around?) network
vulnerabilities
Open Issues
• Measuring delays
– Asymmetry
– round trip is problematic
– triangle inequality doesn’t necessarily hold
• Mapping interfaces to server
• Identifying POPs
• Identifying motiffs