ad hoc拓扑控制算法-XTC

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Conclusions
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XTC Algorithm
D C B
•
G
Each node produces “ranking” of neighbors. Examples
– Distance (closest) – Energy (lowest) – Link quality (best)
1. F 3. A 6. D
A
•
E
F
3. E 7. A
1. C 2. E 3. B 4. F 5. D 6. G
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Overview
• • • •
What is Topology Control? Context – related work XTC algorithm XTC analysis
But: exact node positions known
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K-Neigh (Blough, Leoncini, Resta, Santi @ MobiHoc 2003)
• • • “Connect to k closest neighbors!” Very simple algorithm. On average as good as others…
• • •
• •
Relative Neighborhood Graph RNG(V): An edge e = (u,v) is in the RNG(V) iff there is no node w with (u,w) < (u,v) and (v,w) < (u,v).
u
v
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– Worst case – Average case
•
Conclusions
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XTC Analysis (Part 1)
• Symmetry: A node u wants a node v as a neighbor if and only if v wants u. Proof:
– Worst case – Average case
•
Conclusions
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Topology Control
Sometimes also clustering, Dominating Set construction Not in this presentation
• •
Drop long-range neighbors: Reduces interference and energy! But still stay connected (or even spanner)
3. B 4. A 6. G 8. D 2. C 4. G 5. A 4. B 6. A 7. C
D
7. A 8. C 9. E
C B
G
• Each node locally goes through all neighbors in order of their ranking If the candidate (current neighbor) ranks any of your already processed neighbors higher than yourself, then you do not need to connect to the candidate.
– Assume 1) u → v and 2) u ← v – Assumption 2) ⇒ ∃w: (i) w ≺v u and (ii) w ≺u v
•
Contradicts Assumption 1)
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XTC Analysis (Part 1)
• Symmetry: A node u wants a node v as a neighbor if and only if v wants u. Connectivity: If two nodes are connected originally, they will stay so (provided that rankings are based on symmetric link-weights). If the ranking is energy or link quality based, then XTC will choose a topology that routes around walls and obstacles.
1 0 5 10 15 Netw ork Density [nodes per unit disk]
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XTC Average-Case (Geometric Routing)
9 1
worse
8 7 6
connectivity rate GFG/GPSR on GG
0.9 0.8 0.7 Frequency 0.6
XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks
Roger Wattenhofer Aaron Zollinger
Overview
• • • •
What is Topology Control? Context – related work XTC algorithm XTC analysis
0.5
Performance
5 4 3
2
GOAFR+ on GXTC
0.4
0.3 0.2
better
1
GOAFR+ on GG
0
0
0.1 0
5
10
15
Netw ork Density [nodes per unit disk]
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Conclusion
• Even with minimal assumptions, only neighbor ranking, it is possible to construct a topology with provable properties:
Ene rgy cos t - Phas e 1 only
30 25 20 15 10 5 0 10 100 n 1000
– For example: energy to compute K-Neigh topology is much smaller than CBTC topology (figure right)
• Mid-Eighties: randomly distributed nodes
[Takagi & Kleinrock 1984, Hou & Li 1986]
•
Second Wave: constructions from computational geometry, Delaunay Triangulation [Hu 1993], Minimum Spanning Tree [Ramanathan & Rosales-Hain INFOCOM 2000], Gabriel Graph [Rodoplu & Meng 1999] Cone-Based Topology Control
XTC Average-Case
Unit Disk Graph
XTC
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XTC Average-Case (Degrees)
35
30
25
v
Node Degree 20
u
15
UDG max GG max XTC max
10
UDG avg GG avg XTC avg
0 5 10 15 Netw ork Density [nodes per unit disk]
[Wattenhofer et al. INFOCOM 2000];
•
explicitly prove several properties (energy spanner, sparse graph) • Collecting more and more properties
Only neighbor direction and relative distance
too sparse
critical density
too dense
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What’s the value for k at percolation?!? (Tough question?)
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K-Neigh and the Worst Case?
• What if the network looks like this:
k+1 nodes • •
k+1 nodes
Does a typical/average network (or parts of an average network) really look like this? Probably not… but… Still, cool simulation and analysis results by Blough et al.
– – – – Symmetry Connectivity Bounded degree Planarity
Simple algorithm
+
No complex assumptions
XTC lends itself to practical implementation
•
•
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XTC Analysis (Part 2)
• If the given graph is a Unit Disk Graph (no obstacles, nodes homogeneous, but not necessarily uniformly distributed), then … The degree of each node is at most 6. The topology is planar. The graph is a subgraph of the RNG.
[Li et al. PODC 2001, Jia et al. SPAA 2003, Li et al. INFOCOM 2002] (e.g. local, planar, distance and energy spanner, constant node degree [Wang & Li DIALM-POMC 2003])
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Hom ogen K - Neigh CB TC 2/ 3 MS T
Overview
• • • •
What is Topology Control? Context – related work XTC algorithm XTC analysis
– Worst case – Average case
WMAN 2004
Ovet is Topology Control? Context – related work XTC algorithm XTC analysis
– Worst case – Average case
•
Conclusions
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Context – Previous Work
5
0
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XTC Average-Case (Stretch Factor)
1.3
1.25
1.2 Stretch Factor
XTC vs. UDG – Euclidean
1.15
GG vs. UDG – Euclidean
1.1
XTC vs. UDG – Energy
1.05
GG vs. UDG – Energy
A
•
1. C 2. E 3. B 4. F 5. D 6. G
E
• •
F
Not necessarily depending on explicit positions Nodes exchange rankings with neighbors
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XTC Algorithm (Part 2)
[Thanks to P. Santi]
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Tough question: What should k be?
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Percolation
• Node density such that the graph is just about to become connected (about 5 nodes per unit disk).