The Stable Paths Problem and Interdomain Routing Rachit Agarwal - - PowerPoint PPT Presentation

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The Stable Paths Problem and Interdomain Routing Rachit Agarwal - - PowerPoint PPT Presentation

May 31, 2023 321 likes •1.09k views

Problem Formulation A Sufficient Condition for Stability Food for thought! The Stable Paths Problem and Interdomain Routing Rachit Agarwal Results are by others, any errors are by me! Rachit Agarwal The Stable Paths Problem Problem

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SLIDE 1

Problem Formulation A Sufficient Condition for Stability Food for thought!

The Stable Paths Problem and Interdomain Routing

Rachit Agarwal Results are by others, any errors are by me!

Rachit Agarwal The Stable Paths Problem

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SLIDE 2

Problem Formulation A Sufficient Condition for Stability Food for thought!

Outline

1

Problem Formulation

2

A Sufficient Condition for Stability

3

Food for thought!

Rachit Agarwal The Stable Paths Problem

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SLIDE 3

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet

Terminology Autonomous Systems AS ISPs, Companies Set of Routers and links

Rachit Agarwal The Stable Paths Problem

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SLIDE 5

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet

Terminology Autonomous Systems Intra-domain

Rachit Agarwal The Stable Paths Problem

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SLIDE 6

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet

Terminology Autonomous Systems Intra-domain Inter-domain

Rachit Agarwal The Stable Paths Problem

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SLIDE 7

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet Architecture

Non-cooperative

Rachit Agarwal The Stable Paths Problem

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SLIDE 8

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet Architecture

Non-cooperative Privacy : Do not share Internal Topology

Rachit Agarwal The Stable Paths Problem

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SLIDE 9

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet Architecture

Non-cooperative Privacy : Do not share Internal Topology Policies : Which path to choose? Which path to advertise?

Rachit Agarwal The Stable Paths Problem

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SLIDE 10

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet Architecture

Non-cooperative Privacy : Do not share Internal Topology Policies : Which path to choose? Which path to advertise? Autonomy : Decide policies independently!

Rachit Agarwal The Stable Paths Problem

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SLIDE 11

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Internet Architecture

Non-cooperative Privacy : Do not share Internal Topology Policies : Which path to choose? Which path to advertise? Autonomy : Decide policies independently! Interactive Interact to coordinate Routing

Rachit Agarwal The Stable Paths Problem

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SLIDE 12

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 13

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 14

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d} A path P = (v1 v2)P′ is said to be available for node v1 if P′ has been assigned to v2.

Rachit Agarwal The Stable Paths Problem

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SLIDE 15

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 16

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 17

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 18

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d} Notice Each node behaves selfishly !

Rachit Agarwal The Stable Paths Problem

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SLIDE 19

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d} Notice Each node behaves selfishly ! Each node finds a stable path ! Stable Path No node can get a better path by deviating from the current assignment unilaterally!

Rachit Agarwal The Stable Paths Problem

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SLIDE 20

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d} Notice Each node behaves selfishly ! Each node finds a stable path ! Network is stable! Stable Path No node can get a better path by deviating from the current assignment unilaterally! Nash Eqilibrium!

Rachit Agarwal The Stable Paths Problem

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SLIDE 21

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Example: Good Gadgets

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d} Notice Each node behaves selfishly ! Each node finds a stable path ! Network is stable! Stable Path Assignment! {13d, 2d, 3d, 42d} Stable Path No node can get a better path by deviating from the current assignment unilaterally! Nash Eqilibrium!

Rachit Agarwal The Stable Paths Problem

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SLIDE 22

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 23

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 24

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 2d 342d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 25

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 2d 342d 42d 1d 21d 342d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 26

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 21d 342d 42d 1d 21d 342d ǫ

Rachit Agarwal The Stable Paths Problem

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SLIDE 27

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 21d 342d ǫ 1d 21d 3d ǫ

Rachit Agarwal The Stable Paths Problem

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SLIDE 28

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 21d 3d ǫ 13d 21d 3d 43d

Rachit Agarwal The Stable Paths Problem

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SLIDE 29

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 13d 21d 3d 43d 13d 2d 3d 43d

Rachit Agarwal The Stable Paths Problem

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SLIDE 30

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 13d 2d 3d 43d 13d 2d 3d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 31

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 13d 2d 3d 42d 13d 2d 342d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 32

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 13d 2d 342d 42d 1d 2d 342d 42d

Rachit Agarwal The Stable Paths Problem

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SLIDE 33

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Bad Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} 1d 2d 342d 42d 1d 2d 342d 42d ⋆ The network may not have a stable path assignment (stable state).

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Naughty Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Stable State 13d 2d 3d 43d

Rachit Agarwal The Stable Paths Problem

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SLIDE 35

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Naughty Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Stable State 13d 2d 3d 43d Naughty Still Diverges!

Rachit Agarwal The Stable Paths Problem

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SLIDE 36

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Naughty Gadgets

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Stable State 13d 2d 3d 43d Naughty Still Diverges! ⋆ ⋆ A network may not stabilize even if the network has a stable state.

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Why is the Problem Important?

Rachit Agarwal The Stable Paths Problem

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SLIDE 38

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Why is the Problem Important?

Figure: Good Gadget

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 39

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Why is the Problem Important?

Figure: Good Gadget

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Figure: Bad Gadget

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 40

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Why is the Problem Important?

Figure: Good Gadget

d {13d, 1d} 1 2 {21d, 2d} {3d, 342d} 3 4 {42d, 43d}

Figure: Bad Gadget

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {42d, 43d} A simple configuration error may lead to a complete outage!

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Stable Paths Problem

An instance I = (G, P, Λ) of a Stable Paths Problem is: An undirected graph G = (V , E) A set of permissible paths Pu for each node u ∈ V For each path P ∈ Pu, node u has a ranking λu(P) based on ‘local’ preferences A “destination” node d ∈ V Path Assignment π = {π(u)|u ∈ V \d}.

Rachit Agarwal The Stable Paths Problem

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SLIDE 42

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Stable Paths Problem

An instance I = (G, P, Λ) of a Stable Paths Problem is: An undirected graph G = (V , E) A set of permissible paths Pu for each node u ∈ V For each path P ∈ Pu, node u has a ranking λu(P) based on ‘local’ preferences A “destination” node d ∈ V Path Assignment π = {π(u)|u ∈ V \d}. choices(π, u) = {(u v)π(v)|(u v) ∈ E} ∩ Pu if u = d (d)

  • therwise

A solution to a given instance of Stable Paths Problem is: A path assignment π such that each node is assigned its highest ranked path among the set of paths choices(π, u).

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

More on Stable-Paths Problem

Employed in inter-domain routing Routing protocol that implements Stable Paths Problem: BGP

Rachit Agarwal The Stable Paths Problem

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SLIDE 44

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

More on Stable-Paths Problem

Employed in inter-domain routing Routing protocol that implements Stable Paths Problem: BGP ⋆ Not every instance of Stable-Paths Problem has a solution.

Rachit Agarwal The Stable Paths Problem

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SLIDE 45

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Problem

Fundamental Question Given I = (G, P, Λ), can stability be guaranteed?

Rachit Agarwal The Stable Paths Problem

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SLIDE 46

Problem Formulation A Sufficient Condition for Stability Food for thought! Routing in the Internet Problem Statement

Problem

Fundamental Question Given I = (G, P, Λ), can stability be guaranteed? No, if each node can be assigned only one path to the destination!

Rachit Agarwal The Stable Paths Problem

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SLIDE 47

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: d

Rachit Agarwal The Stable Paths Problem

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SLIDE 48

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk d u0 u3 u1 u2

Rachit Agarwal The Stable Paths Problem

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SLIDE 49

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk A sequence of paths Q0, Q1, . . . , Qk d u0 u3 u1 u2 Q0 Q1 Q2 Q3

Rachit Agarwal The Stable Paths Problem

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SLIDE 50

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk A sequence of paths Q0, Q1, . . . , Qk A sequence of paths R0, R1, . . . , Rk such that d u0 u3 u1 u2 Q0 Q1 Q2 Q3 R0 R1 R3 R2

Rachit Agarwal The Stable Paths Problem

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SLIDE 51

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk A sequence of paths Q0, Q1, . . . , Qk A sequence of paths R0, R1, . . . , Rk such that Ri is a path from ui to ui+1 d u0 u3 u1 u2 R0

Rachit Agarwal The Stable Paths Problem

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SLIDE 52

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk A sequence of paths Q0, Q1, . . . , Qk A sequence of paths R0, R1, . . . , Rk such that Ri is a path from ui to ui+1 Qi ∈ Pui , RiQi+1 ∈ Pui d u0 R0 Q0 Q1

Rachit Agarwal The Stable Paths Problem

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SLIDE 53

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Dispute Wheel

A dispute wheel W is: A sequence of nodes u0, u1, . . . , uk A sequence of paths Q0, Q1, . . . , Qk A sequence of paths R0, R1, . . . , Rk such that Ri is a path from ui to ui+1 Qi ∈ Pui , RiQi+1 ∈ Pui λui (Qi) < λui (RiQi+1) d u0 R0 Q0 Q1

Rachit Agarwal The Stable Paths Problem

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SLIDE 54

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 55

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Consider node 1 (u0) W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 56

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Consider node 1 (u0) Q0 : 1d W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 57

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Consider node 1 (u0) Q0 : 1d R0 : 13, Q1 : 3d W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 58

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Consider node 1 (u0) Q0 : 1d R0 : 13, Q1 : 3d R0Q1 : 13d W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 59

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Dispute Wheel

d {13d, 1d} 1 2 {21d, 2d} {342d, 3d} 3 4 {43d, 42d} Consider node 1 (u0) Q0 : 1d R0 : 13, Q1 : 3d R0Q1 : 13d λ1(1d) < λ1(13d) W = {{1, 3, 2}, {1d, 3d, 2d}, {13, 342, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 60

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Multiple Minimal Dispute Wheels

d 1 {123d, 12d, 1d} {231d, 23d, 2d} 2 3 {312d, 31d, 3d}

Rachit Agarwal The Stable Paths Problem

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SLIDE 61

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Multiple Minimal Dispute Wheels

d 1 {123d, 12d, 1d} {231d, 23d, 2d} 2 3 {312d, 31d, 3d} d 1 2 3 {{1, 2, 3}, {1d, 2d, 3d}, {12, 23, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 62

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Multiple Minimal Dispute Wheels

d 1 {123d, 12d, 1d} {231d, 23d, 2d} 2 3 {312d, 31d, 3d} d 1 2 3 {{1, 2, 3}, {1d, 2d, 3d}, {12, 23, 21}} d 1 2 {{1, 2}, {1d, 2d}, {12, 21}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 63

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Multiple Minimal Dispute Wheels

d 1 {123d, 12d, 1d} {231d, 23d, 2d} 2 3 {312d, 31d, 3d} d 1 2 3 {{1, 2, 3}, {1d, 2d, 3d}, {12, 23, 21}} d 1 2 {{1, 2}, {1d, 2d}, {12, 21}} d 1 3 {{1, 3}, {1d, 3d}, {13, 31}}

Rachit Agarwal The Stable Paths Problem

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SLIDE 64

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Example: Multiple Minimal Dispute Wheels

d 1 {123d, 12d, 1d} {231d, 23d, 2d} 2 3 {312d, 31d, 3d} d 1 2 3 {{1, 2, 3}, {1d, 2d, 3d}, {12, 23, 21}} d 1 2 {{1, 2}, {1d, 2d}, {12, 21}} d 1 3 {{1, 3}, {1d, 3d}, {13, 31}} d 2 3 {{2, 3}, {2d, 3d}, {23, 312}}

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Stability

Stability An instance I is SPP-solvable if there is no dispute wheel in I.

Rachit Agarwal The Stable Paths Problem

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SLIDE 66

Problem Formulation A Sufficient Condition for Stability Food for thought! Dispute Wheels Sufficient Condition for Stability

Stability

Stability An instance I is SPP-solvable if there is no dispute wheel in I. Sufficient condition, not necessary!

Rachit Agarwal The Stable Paths Problem

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SLIDE 67

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Food for thought!

Rachit Agarwal The Stable Paths Problem

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SLIDE 68

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Food for thought!

Should we really be concerned about the problem (how often do disputes occur anyways?)

Rachit Agarwal The Stable Paths Problem

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SLIDE 69

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Food for thought!

Should we really be concerned about the problem (how often do disputes occur anyways?) Should we be using BGP?

Rachit Agarwal The Stable Paths Problem

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SLIDE 70

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Food for thought!

Should we really be concerned about the problem (how often do disputes occur anyways?) Should we be using BGP? How could we guarantee stability?

Rachit Agarwal The Stable Paths Problem

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SLIDE 71

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Impossibility Results

Stable Paths Problem Given I, it is NP-hard to decide if the network is SPP-solvable. Other Negative Results Any protocol that guarantees solvability of I has to be a generalization of Shortest-Path Routing.

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Gao-Rexford Policies

Restriction on Paths Prefer customer routes over peer or provider routes Export only customer routes to peers or providers No cycle of customer-provider relationships

Rachit Agarwal The Stable Paths Problem

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SLIDE 73

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Dynamic Dispute Detection

Routing Anomalies (Revoking Autonomy) Nodes can detect persistent oscillations and change their preferences resulting in Λ guaranteeing SPP-solvability. A node routes its own and neighbors’ traffic through a non-preferred path.

Rachit Agarwal The Stable Paths Problem

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SLIDE 74

Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Multipath Solutions

NS-BGP (Multipath, Restriction on Paths) Assigns multiple paths to a node, where a node’s neighbor may route traffic through one of the paths assigned to this node. Multi-path routing can help! Not completely. Fractional-BGP (Multipath, Hard Problem) An abstract model in which nodes may be assigned exponentially many paths Non-constructive proof of every I being Fractional-BGP solvable. Not so efficient (finding a Fractional-BGP solution is ’hard’) Multi-path routing is stable!

Rachit Agarwal The Stable Paths Problem

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Problem Formulation A Sufficient Condition for Stability Food for thought! Related works

Which one would you use?

?

Rachit Agarwal The Stable Paths Problem