routing state distance: a path-based metric for network analysis natali ruchansky gonca gürsun,...
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Routing State Distance:A Path-based Metric for
Network Analysis
Natali Ruchansky
Gonca Gürsun, Evimaria Terzi, and Mark Crovella
Based on this distance intuition we develop a new metric based on paths and show it is good for:
oVisualization of networks and routesoCharacterizing routesoDetecting significant patternsoGaining insight about routing
A New Metric
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Conceptually…
• Imagine capturing the entire interdomain routing state of the internet in a matrix
the next hop on path from to
• Each row is the routing table of a single AS• Now consider the columns…
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𝑵=[¿¿]SourcesDestination
s
We define between two prefixes and as the number of entries that differ in their
columns of
Routing State Distance
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i.e. the number of ASesthat disagree about the next-hop to and .
More Formally
Given a universe of prefixes define:
A next-hop matrix : the next-hop on the path to
As well as :
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RSD to BGP
In order to apply to measured BGP paths we define to have ASes on rows and prefixes on columns.
the next-hop from AS to prefix
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Solution Key: is defined on a setof paths NOT a graph
A few issues arise…1. Missing Values2. Multiple next hops
Our Data
From 48 million AS paths consisting of:
359 unique monitors450K destination prefixes
We end up with:
243 sources ASes 130K prefixes
Thus our is
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Finer Grained Measure
Varies smoothly and has a gradual slope. Allows fine
granularity12
Increase of 1 encompasses many prefixes
1. Highly structured 2. Allows 2D
visualization
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From compute , our distance matrix where:𝑫 (𝒙𝟏 , 𝒙𝟐)=𝑹𝑺𝑫(𝒙𝟏 ,𝒙𝟐)
Yeah, but a cluster of what!?!
Now in routing terms:o Any row in must have the
same next hop in nearly each cell
o The set of ASes make similar routing decisions w.r.t destinations
First think matrix-wise ():o A cluster corresponds to a set
of columns o Columns being close in
means they are similar in some positions
o is highly coherent
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We call such a pair a local atom
A local atom is a set of prefixes that are routed similarly in some region of
the internet.
So the smaller cluster is a local atom of certain prefixes that are routed similarly
by a large set of ASes
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For this investigate … • Prefer a specific AS for transit to these
prefixes. Hurricane Electric (HE)• If any path passes through HE :
1. Source ASes prefer that path2. Prefix appears in the smaller cluster
.
Why these specific prefixes?
Level3 Hurricane Electric Sprint
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But why do sources always route through HE if the option exists?
….HE has a relatively unique peering policy.
Offer peering to ANY AS with presence in the same exchange point.
HE’s peers prefer using HE for ANY customer of HEAnd hence consists of networks that peer with HE,
and consists of HE’s customers
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Analysis with uncovered a macroscopic atom
Can we formulate a systematic study to uncover other smaller atoms?
Intuitively we would like a partitioning of the prefixes such that :
oIn the same group is minimizedoBetween different groups is
maximized
Can We Find More Clusters?
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RS-Clustering Problem
Intuition: A partitioning of the prefixes such that :oIn the same group is minimizedoBetween different groups is maximized
For a partition :
Key Advantage: Parameter Free!
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Optimal is Hard
Finding the optimal solution to the Problem is NP-hard
We propose two approaches:Pivot Clustering
Overlap Clustering
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Given a set of prefixes , their values, and a threshold parameter :
1. Start from a random prefix (the pivot)2. Find all that fall within distance to and
form a cluster3. Remove cluster from and repeat
Advantages:o The algorithm is fast : O(|E|)o Provable approximation guarantee
Pivot Clustering Algorithm
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Size of C Size of S Destinations
C1 150 16 Ukraine 83%Czech. Rep 10%
C2 170 9 Romania 33%Poland 33%
C3 126 7 India 93%US 2%
C4 484 8 Russia 73%Czech rep. 10%
C5 375 15 US 74%Australia 16%
Interpreting Clusters
To address this we propose a formalism called Overlap
Clustering and show that it is capable of extracting such clusters.
We ask ourselves if a partition is really
best?
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Seek a clustering that captures overlap
Related Work• Reported that BGP tables provide an incomplete view
of the AS graph.[Roughan et. al. ‘11]
• Visualization based on AS degree and geo-location. [Huffaker and k. claffy ‘10]
• Small scale visualization through BGPlay and bgpviz
• Clustering on the inferred AS graph.[Gkantsidis et. al. ‘03]
• Grouping prefixes that share the same BGP paths into policy atoms.[Broido and k. claffy ‘01]
• Methods for calculating policy atoms and characteristics.[Afek et. al. ‘02] 2
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Take-AwayAnalysis with typical distance metrics is hard
We introduce a new one
-- Routing State Distance – that is simple and based only on paths
Overcome BGP hurdles and show it can be used for:o In-depth analysis of BGPo Capturing closeness useful for visualizationo Uncovering surprising patternso General setting
Developed a new set of tools forextracting insight from BGP measurements
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Code, data, and more information is available on our website at:
csr.bu.edu/rsd
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Code• Pivot Clustering• Overlap Clustering• RSD Computation
Data• Prefix List• Pairwise RSD
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