spanning tree method for link state aggregation in large communication networks whay choiu lee
DESCRIPTION
Introduction Why is the link state aggregation needed? Complexity of link state updates( O(n 2 ) ). Security. Criteria of desirable link state aggregation: Adequately represents the original network. Significantly compresses the original network.TRANSCRIPT
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Spanning Tree Method for Link State Aggregation in Large Communication
Networks
Whay Choiu Lee
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Overview
IntroductionExisting methods for link state aggregation
symmetric-pointfull-meshstar
Spanning Tree Methodintuitionproperties of spanning treehow does it work
DiscussionSummary
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Introduction
Why is the link state aggregation needed? Complexity of link state updates( O(n2) ). Security.
Criteria of desirable link state aggregation: Adequately represents the original network. Significantly compresses the original network.
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Introduction
Common solution for complexity reduction Hierarchical structure.
Boarder nodes Logical links
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Subnetwork Topology
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
(bandwidth, delay)
non-additive, additive
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Existing methods for link state aggregation
Symmetric-point
Pro:greatest reduction.O(1).
Con:does not adequately reflect
any asymmetric topology.does not capture any multiple
connectivity.
(2,30)
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
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Existing methods for link state aggregation
Full-Mesh
Pro:adequate
representation.flexibility.
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)A B
CD(6,24)
(7,17)
(6,21)
(4,27)
(4,13)
Con:link state explosion.O(n2).
(4,18)
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Existing methods for link state aggregation
Star
Pro:limited flexibility.O(n).
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)A B
CD
Con:does not capture any multiple
connectivity.
(1,15)
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Spanning tree method
Idea: Represent the original subnetwork by full-mesh topology
consisting of predetermined subset of the nodes. Encode the link state information associated with the full-
mesh representation. Advantages:
O(n). Link state of nodes not on spanning tree may be derived or
estimated. Multiple connectivity.
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Spanning tree method
Properties of spanning tree: Tree: connecting set of nodes with no loop. G(N, N-1). Unique path connecting each pair of nodes. Maximum spanning tree vs. minimum spanning tree.
Maximum weight spanning tree:d <= min(a,b,c)
Minimum weight spanning tree:d >= max(a,b,c)
A B
CD
b a d c
Spanning Tree
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Spanning tree method
1. Determine maximum bandwidth path for each pair of border nodes.
2. Create logical link between each pair of border nodes to form a full-mesh, and assign it the (bandwidth, delay) of maximum bandwidth path.
3. Generate one maximum weight spanning tree based on bandwidth, and another based on delay.
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)D-B (4,27)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)D-B (4,27)D-C (6, 21)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
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Constructing Maximum-Bandwidth Full-Mesh Representation
shortest-widest routing algorithm
A B
CD
(7,10)
(4,8)
(7,7)
(5,5)
(9,8)
(3,4)
(4,7)
(6,6)
(2,3)
(10,5)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)
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Maximum-Bandwidth Full-Mesh Representation
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)A B
CD
(6,24)
(7,17)
(6,21)
(4,27) (4,18
)
(4,13)
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Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm
Initialize tree T = Ø. Scan links in descending order of
weight. If adding edge E to tree T create a
loop Edge is excluded.
Otherwise, edge is included in Tree T.
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Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)A B
CD
(6,24)
(7,17)
(6,21)
(4,27) (4,18
)
(4,13)
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Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm
A B
CD
(6,24)
(7,17)
(6,21)
(4,27) (4,18
)
(4,13)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)
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Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm
A B
CD
(6,24)
(7,17)
(6,21)
(4,27) (4,18
)
(4,13)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)
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Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm
A B
CD
(6,24)
(7,17)
(6,21)
(4,27) (4,18
)
(4,13)
D-A (7,17)D-B (4,27)D-C (6, 21)
C-A (6, 24)C-B (4, 18)
B-A (4,13)
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Maximum-Weight Spanning Tree for Bandwidth
A B
CD
6
7
6
4 4
4
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Maximum-Weight Spanning Tree for Delay
A B
CD
24
17
21
27 18
13
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Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A
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Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A: E(AD)
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Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A: E(AD), E(AC)
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Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4 = min(6,4)
Root A: E(AD), E(AC), E(CB)
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Decoded Full-Mesh for Bandwidth
A B
CD
6
7
6
4 4
4
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Decoded Full-Mesh for Delay
A B
CD
24
21
21
27 21
21
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Discussion: Full-Mesh Topology Comparison
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
(4,18) c
A B
CD
(6,24) b
(7,17) a
(6,21)
(4,27) d
(4,13)
Maximum-Bandwidth Full-Mesh Decoded Maximum-Bandwidth Full-Mesh
Perfect encoding for bandwidth: d = min(a,b,c)Upper-bound for delay: d <= min(a,b,c)
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Full-Mesh Topology Comparison
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
(4,18) c
A B
CD
(6,24) b
(7,17) a
(6,21)
(4,27) d
(4,13)
Maximum-Bandwidth Full-Mesh Decoded Maximum-Bandwidth Full-Meshmaximum spanning tree: d <= min(a,b,c).
Perfect encoding for bandwidth: d = min(a,b,c)maximum weight full-mesh: d >= min(a,b,c).
Upper-bound for delay: d <= min(a,b,c)
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Discussion: Full-Mesh Topology Problem
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
A B
CD
(2,16)
(7,17)
(3,15)
(2,18) (2,3)
(4,13)
Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh
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Discussion: Full-Mesh Topology Problem
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
A B
CD
(2,16)
(7,17)
(3,15)
(2,18) (2,3)
(4,13)
Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh
Call: C-D (3, 15)
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Discussion: Full-Mesh Topology Problem
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
A B
CD
(2,16)
(7,17)
(3,15)
(2,18) (2,3)
(4,13)
Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh
Call: C-D (3, 15)
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Discussion: Full-Mesh Topology Problem
A B
CD
(6, 24)
(7,21)
(6,21)
(4,27) (4,21
)
(4,21)
A B
CD
(2,16)
(7,17)
(3,15)
(2,18) (2,3)
(4,13)
Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh
Call: C-D (3, 15)
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summary
Spanning tree method Full-mesh topology generation. Spanning tree construction. Topology recovery from spanning tree.
Discussion Perfect encoding vs. upper-bound. Conservative.
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questions