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Routing Algorithms using Random Walks with Tabu Lists
Karine Altisen & Stéphane Devismes
Joint work withAntoine Gerbaud, Pascal Lafourcade,
and Clément Ponsonnet
ARESA 2
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Meeting Synchrone 2
Disclaimer
• Today, we will speak about probabilities– But, we are not specialists …
22/02/11
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Meeting Synchrone 3
Wireless Sensor Network (WSN)
22/02/11
Battery
Sensor(s) Processor Radio
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4
Routing
22/02/11 Meeting Synchrone
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5
Application
22/02/11 Meeting Synchrone
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6
Setting
22/02/11 Meeting Synchrone
48
3
95
61
7
2
• One sink/Multi source
• Connected
• Identified
• Reliable
•Asynchronous
• Spontaneous requests
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Meeting Synchrone 7
Random Walk
22/02/11
48
39
5
6
1
7
2Rand(7,9,2)
Rand(1,7,5,6,2)
Rand(1,9,6)
Rand(9,8,6,4,3)
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8
Probability Laws
• Uniform (RW)– Let v,u two neighbors, v u
– Problem: hitting time = O(N3)
22/02/11 Meeting Synchrone
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Meeting Synchrone 9
Probability Laws
• Biased (Yamashita et al) (RWLD)– Let v,u two neighbors, v u
– standardize frequencies of visits, for all nodes – hitting time = O(N2)
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Meeting Synchrone 10
RW vs. RWLD
22/02/11
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Meeting Synchrone 11
Routing by Random Walk
• Pros– Message length– Tight local computation and memory– No need of overlay– Load of the network– …
• Cons– Hitting time
• (average number of hops to reach the sink) • O(N3) (RW) and O(N2) (RWLD)
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Meeting Synchrone 12
Random Walk with Tabu Lists
• Add memory to help random walks– Avoid cycles
• Store hints about previous choices
• ≤k where k is small– Good trade-off ?
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Meeting Synchrone 13
Where ?
• Messages– Store IDs of visited nodes– Visit new nodes first
• Nodes– One list per destination– Store message ID– Detect cycles– cycle detections: visits
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Meeting Synchrone 14
Full ? (Update policy)
• FIFO policy
• Rand policy
22/02/11
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Meeting Synchrone 15
FIFO Policy
• Update(e,L)
22/02/11
a b e d
a b d e
a b f d g z
e
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Meeting Synchrone 16
Rand Policy
• Update(e,L)
22/02/11
a b d e
a b f d g z e
Rand
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Meeting Synchrone 17
Sum up
• Probability law: RW / RWLD
• Tabu Lists Location: node / message
• Tabu List size
• Update policies: FIFO / Rand
22/02/11
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Meeting Synchrone 18
Tabu List in Messages (TLM)
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48
39
5
6
1
7
2Rand(7,9,2)=2
Rand(7,5,6)=5
Rand(9,6) = 9
Rand(8,6,4,3) = 3
[1]
[1][1,2]
[1,2][2,9]
[2,9][9,5]
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Meeting Synchrone 19
Tabu List & Counters in Nodes (TLCN)(1/2)
22/02/11
121
1
1
1
(12,1)
1
(12,1)
(23,8) (23,8)
(12,1)
(23,8)
(23,8)2
2
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Meeting Synchrone 20
Tabu List & Counters in Nodes (TLCN)(2/2)
• Next destination ?
22/02/11
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Meeting Synchrone 21
Experimentations (settings)
• Sinalgo (JAVA)• Graphs: UDG, connected, one sink/multi-source, uniform
distribution• 100 messages per sources• Data generation: [400..600]• Transmission time: [40..50]• List sizes:
– TLM: 1 & 15– TLCN: 15
• Random Walk: RWLD• Update: FIFO & Rand 22/02/11
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Meeting Synchrone 22
Hitting time (1/2)
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Meeting Synchrone 23
Hitting time (2/2)
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Meeting Synchrone 24
Volume, e.g., sum |messages|
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Meeting Synchrone 25
Convergence of TLCN
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Meeting Synchrone 26
Sum up
22/02/11
Hitting Time Volume Degree Sensitivity
Load Sensitivity
TLCN (15,FIFO) 1 1 no yes
TLCN (15,Rand) 1 1 no yes
TLM (15,FIFO) 3 7 no no
TLM (15,Rand) 4 8 no no
TLM (1,FIFO) 5 5 no no
TLM (1,Rand) 6 6 no no
RWLD 7 3 no no
RW 8 4 yes no
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Meeting Synchrone 27
Analysis
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Meeting Synchrone 28
NSC for TLM
• NSC: update rule finite average hitting time
“If the list is full and the current node is not in the list, then the probability of removing the oldest element is positive”
FIFO and Rand match the NSC
22/02/11
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29
RW+TLM vs. RW (1/2)
• |List| ≥ 3, there exist graphs where RW is better than RW+TLM
• Ex. for 4
22/02/11 Meeting Synchrone
…
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Meeting Synchrone 30
RW+TLM vs. RW (2/2)
• |List| = 1,2, RW+TLM is always better than RW
22/02/11
147932
RW+TLM
RW
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Meeting Synchrone 31
RWLD+TLM vs. RWLD (1/2)
• For all size, there exist graphs where RWLD is better than RWLD+TLM– |List| ≥ 3, as previously– 2, to be done !– 1:
22/02/11
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Meeting Synchrone 32
RWLD+TLM vs. RWLD (2/2)
• Conjecture: In random graphs, RWLD+TLM is always better than RWLD
22/02/11
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Meeting Synchrone 33
RW+TLM 1,2 vs. RWLD (2/2)
• There exist graphs where RWLD is better than RW+TLM
22/02/11
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34
TLCN
• Is the hitting time finite ? In case ∞+asynchronous, no
22/02/11 Meeting Synchrone
Sink
Source
∞1
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Meeting Synchrone 35
Thank you
22/02/11