Compact Routing Schemes Mikkel Thorup, Uri Zwick Ankit Singla CS - - PowerPoint PPT Presentation

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Compact Routing Schemes Mikkel Thorup, Uri Zwick Ankit Singla CS 598 Oct. 20, 2009 Ankit Singla (CS 598) Compact Routing Schemes Oct. 20, 2009 1 / 13 The Extremes Complete (n) size route tables (Image Credits: Geoff Houston @

SLIDE 1

Compact Routing Schemes

Mikkel Thorup, Uri Zwick Ankit Singla

CS 598

Oct. 20, 2009

Ankit Singla (CS 598) Compact Routing Schemes

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SLIDE 2

The Extremes

Complete Ω(n) size route tables (Image Credits: Geoff Houston @ potaroo.net) Source routing with Ω(n) packet headers

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SLIDE 3

A Mid-way Approach

˜ O(√n) routing tables at nodes (1 + o(1)) log2 n -bit node headers Constant time routing decisions at nodes

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SLIDE 4

A Mid-way Approach

˜ O(√n) routing tables at nodes (1 + o(1)) log2 n -bit node headers Constant time routing decisions at nodes Bounded increase in path length!

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SLIDE 5

Centers

Pick a set of ‘centers’ A

These images are from Zwick’s slides

centA(v) is the center closest to v

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SLIDE 6

Clusters

clusterA(w) is the set of nodes closer to w than to any center

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SLIDE 7

State at a Node

Every node v stores Shortest paths to all centers Shortest paths to all nodes in clusterA(v)

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SLIDE 8

Routing Method

For routing a message from u to v Case: v ∈ clusterA(u) Route directly since shortest path is stored at v Case: v / ∈ clusterA(u) Route through centA(v) - shortest path to centA(v), from there to v

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SLIDE 9

Picking Centers

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SLIDE 10

Stretch-3 Proof

If v ∈ clusterA(u), stretch = 1; Otherwise the following theorem holds Theorem δ(u, centA(v)) + δ(centA(v), v) ≤ 3 * δ(u, v)

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SLIDE 11

Stretch-3 Proof

If v ∈ clusterA(u), stretch = 1; Otherwise the following theorem holds Theorem δ(u, centA(v)) + δ(centA(v), v) ≤ 3 * δ(u, v) Triangle inequality - δ(u, centA(v)) ≤ δ(u, v) + δ(v, centA(v))

Ankit Singla (CS 598) Compact Routing Schemes

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SLIDE 12

Stretch-3 Proof

If v ∈ clusterA(u), stretch = 1; Otherwise the following theorem holds Theorem δ(u, centA(v)) + δ(centA(v), v) ≤ 3 * δ(u, v) Triangle inequality - δ(u, centA(v)) ≤ δ(u, v) + δ(v, centA(v)) Symmetry - δ(v, centA(v)) = δ(centA(v), v)

Ankit Singla (CS 598) Compact Routing Schemes

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SLIDE 13

Stretch-3 Proof

If v ∈ clusterA(u), stretch = 1; Otherwise the following theorem holds Theorem δ(u, centA(v)) + δ(centA(v), v) ≤ 3 * δ(u, v) Triangle inequality - δ(u, centA(v)) ≤ δ(u, v) + δ(v, centA(v)) Symmetry - δ(v, centA(v)) = δ(centA(v), v) Since v / ∈ clusterA(u), δ(centA(v), v) ≤ δ(u, v)

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SLIDE 14

Routing Decision Time and Header Size

Node v’s label contains (v, centA(v), port(centA(v), v)) This label is carried in every message to v Use hash table at every node w, containing (v, port(w, v)) ∀v ∈ A ∪ clusterA(w)

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SLIDE 15

Routing Decision Time and Header Size

Node v’s label contains (v, centA(v), port(centA(v), v)) This label is carried in every message to v Use hash table at every node w, containing (v, port(w, v)) ∀v ∈ A ∪ clusterA(w) Header size reduction depends on clever ordering and labeling of nodes and ports

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SLIDE 16

Tree Routing, Handshaking and All That Jazz ...

Stretch 2k - 1 requires O(n1/k) state at routers This involves use of more ‘loose’ structure than the global centers - tree covers!

Each router is included in a bounded number of trees Each pair is connected by a stretch 2k - 1 path in at least one tree Tree routing algorithms are then used on this tree cover

Handshaking: exchange of information after which the stretch 2k - 1 path becomes known

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SLIDE 17

Discussion?

How practical are the header size reduction methods? What issues must be addressed before this can be deployed? What changes with mobility of nodes?

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SLIDE 18

Thank You!

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