On Inferring Autonomous System Relationships in the Internet

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On Inferring Autonomous System Relationships in
the Internet

• Lixin Gao, Member, IEEE
• IEEE/ACM transactions on networking 2001

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Outline

• Internet Architecture
• Routing Policies
• AS Relationship and Routing Table Entry Patterns
• Algorithm -- Basic, Refined, Final
• Experimental Result

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Internet Architecture

• We can model the connectivity between ASs in the
  Internet
• using an AS graph , where the node set consists
  of ASs and
• the edge set consists of AS pairs that exchange
• traffic with each other.

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Routing Policies and BGP Routing Tables
702
701
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1849
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• Import policy Export policy
• import(u,v)R represents AS vs update set
  after applying the import policy to the
  update routes R received
• from AS u
• export(v,u)R represent the route set R which
  is sent by AS
• u to its
  neighboring AS v according to us
• export policy
• B(u,d) the best route selected by AS u for
  prefix d

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• e(u,d) The routing table entry in AS u for
  destination d is a
• route with empty AS path if u originates
  prefix d
• The routing table entries of AS u for destination
  prefix d

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AS Relationships

• An annotated AS graph is a partially
• directed graph whose
• nodes represent ASs
• and whose edges are
• classified into
• provider-to-customer, customer-to-provider,
  peer-to-peer and
• sibling-to-sibling edges.

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AS Relationships

• ASs u and v have a peering relationship iff
  neither u transits
• traffic for v nor v transits traffic for
  u.
• AS u is a provider of AS v iff u transits
  traffic for v and v
• does not transit traffic for u.
• ASs u and v have a sibling relationship iff both
  u transits
• traffic for v and v transits traffic for u.

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• provder-to-customer (customer-to-provider or
  peer-to-peer or sibling-to-sibling) edge
• When traversing an edge from a customer to a
  provider,
• we refer to the edge as a customer-to-provider
  edge.

Customer
Provider
AS
AS
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• customer (provider, or peer) route
• Let r.as_path (u1,u2,un)
• If (ui,ui1) is a sibling-to-sibling edge for
  all ilt j and (uj,uj1)
• is a provider-to-customer
  (customer-to-provider or peer-to-peer) edge, then
  r is a customer(provider or peer) route.

sibling-to-sibling edge
provider-to-customer edge
AS 1
AS
AS
AS j
AS j!
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BGP export policy
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Selective Export Rule
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Velley-Free

• Valley-Free After traversing a
  provider-to-customer or
• peer-to-peer edge, the AS path
  cannot traverse a
• customer-to-provider or
  peer-to-peer edge.
• That is,

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Not Valley-Free

• 1. 2.
• 3. 4.

peer-to-peer
peer-to-peer
peer-to-peer
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Example of Valley-Free
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• Theorem 3.1
• If all ASs set their export policies
  according to the selective export rule, then the
  AS path in any BGP routing table entry is
  valley-free.
• Downhill Path A sequence of edges that are
  either provider-
• to-customer or sibling-to-sibling
  edges.
• Uphill Path A sequence of edges that are either
  customer-
• to-provider or sibling-to-sibling edges.

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• Corollary 3.1
• An AS path of a BGP routing table entry has one
  of the following patterns
• 1) an uphill path
• 2) a downhill path
• 3) an uphill path followed by a downhill path
• 4) an uphill path followed by a peer-to-peer
  edge
• 5) a peer-to-peer edge followed by a downhill
  path or
• 6) an uphill path followed by a peer-to-peer
  edge, which is
• followed by a downhill path.

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• Maximal Uphill Path The longest uphill path in
  the AS path.
• Maximal Downhill Path The remaining AS path
  after
• removing the maximal uphill path and the
  peer-to-
• peer edge.
• Uphill Top Provider the last AS in its maximal
  uphill path
• Downhill Top Provider the first AS in its
  maximal downhill path
• Top Provider is an AS that has the heighest
  degree among all Ass in the AS path

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Uphill Top Provider
Downhill Top Provider
ui
Ui1
Un-1
u2
un
u1
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Basic Algorithm

• Our algorithms are based on the intuition that a
  provider typically has a larger size than its
  customer does and the size of an AS is typically
  proportional to its degree in the AS graph.
• consecutive AS pairs that appear before the top
  provider in the AS path are customer-to-provider
  or sibling-to-sibling edges, and consecutive
  pairs that appear after the top provider in the
  AS path are provider-to-customer or
  sibling-to-sibling edges.
• We then identify peer-to-peer edges from the set
  of AS pairs that appear only as the top provider
  and the top providers neighbor in an AS path.

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uj
uj1
u2
un-1
u1
un
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ub
ua
uc
uj
uj1
ud
u2
un-1
u1
un
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ub
ua
uc
ud
u2
u1
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ub
ua
uc
uj
uj1
ud
u2
un-1
Sibling-siblingu1,u2 1
u1
un
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Rifined Algorithm

• In the refined algorithm, we assume that
  misconfigured BGP speaking routers affect only a
  small number of routing table entries.
• EX.
  ( u, w, v )
• Specifically, we use the heuristic that if no
  more than L routing table entries infer that AS u
  provides transit services for AS v and more than
  L routing table entries infer that AS v provides
  transit services for AS u, then we ignore the
  routing table entries that infer that AS u
  transits for AS v and we conclude that u is a
  customer of v, where L is a small constant.

u
v
w
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Final Algorithm

• According to Corollary 3.1, if an AS pair appear
  consecutively
• in an AS path and neither of the AS pair is the
  top provider of
• the AS path, then the AS pair have a transit
  relationship and
• therefore, the AS pair do not have a peering
  relationship.
• According to Corollary 3.1, an AS path has at
  most one consecutive AS pair that have a peering
  relationship.
• That is, a top provider can have a peering
  relationship with at most one of its neighbors in
  the AS path.

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Final Algorithm

• Since we might not have routing tables from all
  BGP speaking routers, we might not be able to
  identify all AS pairs that do not have peering
  relationships using the heuristic described
• above.
• We assume that the degrees of the two ASs that
  have a peering relationship do not differ by more
  than R times, where R is a constant.

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Experimental Results
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Verifications by the WHOIS Sever

• Since the WHOIS lookup service supplies the name
  and address of the company that owns an AS
• confirm that an AS pair has a sibling
  relationship
• if the two ASs belong to the same company or two
  merging companies (such as ATT and Cerfnet).
• if the ASs belong to two small companies that are
  located in the same city (which increases the
  likelihood that they have a mutual-transit
  agreement).
• We manually queried the WHOIS lookup service and
  confirmed 101 of 186 ( 54.3 )inferred sibling
  relationships for the January 2, 2000 data.