Routing Algorithms using Random Walks with Tabu Lists

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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Disclaimer

• Today, we will speak about probabilities– But, we are not specialists …

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Wireless Sensor Network (WSN)

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Battery

Sensor(s) Processor Radio

4

Routing

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5

Application

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6

Setting

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48

3

95

61

7

2

• One sink/Multi source

• Connected

• Identified

• Reliable

•Asynchronous

• Spontaneous requests

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Random Walk

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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)

8

Probability Laws

• Uniform (RW)– Let v,u two neighbors, v u

– Problem: hitting time = O(N3)

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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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RW vs. RWLD

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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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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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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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Full ? (Update policy)

• FIFO policy

• Rand policy

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FIFO Policy

• Update(e,L)

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a b e d

a b d e

a b f d g z

e

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Rand Policy

• Update(e,L)

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a b d e

a b f d g z e

Rand

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Sum up

• Probability law: RW / RWLD

• Tabu Lists Location: node / message

• Tabu List size

• Update policies: FIFO / Rand

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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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Tabu List & Counters in Nodes (TLCN)(1/2)

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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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Tabu List & Counters in Nodes (TLCN)(2/2)

• Next destination ?

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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

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Hitting time (1/2)

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Hitting time (2/2)

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Volume, e.g., sum |messages|

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Convergence of TLCN

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Sum up

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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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Analysis

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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

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RW+TLM vs. RW (1/2)

• |List| ≥ 3, there exist graphs where RW is better than RW+TLM

• Ex. for 4

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…

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RW+TLM vs. RW (2/2)

• |List| = 1,2, RW+TLM is always better than RW

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147932

RW+TLM

RW

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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:

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RWLD+TLM vs. RWLD (2/2)

• Conjecture: In random graphs, RWLD+TLM is always better than RWLD

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RW+TLM 1,2 vs. RWLD (2/2)

• There exist graphs where RWLD is better than RW+TLM

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TLCN

• Is the hitting time finite ? In case ∞+asynchronous, no

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Sink

Source

∞1

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Thank you22/02/11