Spanning Tree Method for Link State Aggregation in Large Communication Networks Whay Choiu Lee.
-
Upload
emma-townsend -
Category
Documents
-
view
217 -
download
0
description
Transcript of Spanning Tree Method for Link State Aggregation in Large Communication Networks Whay Choiu Lee.
Spanning Tree Method for Link State Aggregation in Large Communication
Networks
Whay Choiu Lee
Overview
IntroductionExisting methods for link state aggregation
symmetric-pointfull-meshstar
Spanning Tree Methodintuitionproperties of spanning treehow does it work
DiscussionSummary
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.
Introduction
Common solution for complexity reduction Hierarchical structure.
Boarder nodes Logical links
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
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)
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)
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)
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.
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
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.
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)
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)
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)
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)
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)
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)
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)
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)
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.
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)
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)
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)
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)
Maximum-Weight Spanning Tree for Bandwidth
A B
CD
6
7
6
4 4
4
Maximum-Weight Spanning Tree for Delay
A B
CD
24
17
21
27 18
13
Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A
Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A: E(AD)
Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search
A B
CD
6
7
6
4 4
4
Root A: E(AD), E(AC)
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)
Decoded Full-Mesh for Bandwidth
A B
CD
6
7
6
4 4
4
Decoded Full-Mesh for Delay
A B
CD
24
21
21
27 21
21
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)
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)
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
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)
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)
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)
summary
Spanning tree method Full-mesh topology generation. Spanning tree construction. Topology recovery from spanning tree.
Discussion Perfect encoding vs. upper-bound. Conservative.
questions