Routing Algorithms using Random Walks with Tabu Lists

Karine Altisen & Stéphane Devismes

Joint work withAntoine Gerbaud, Pascal Lafourcade, and

Clément Ponsonnet

ARESA 2

Meeting Synchrone 2

Disclaimer

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

22/02/11

Meeting Synchrone 3

Wireless Sensor Network (WSN)

22/02/11

Battery

Sensor(s) Processor Radio

4

Routing

22/02/11 Meeting Synchrone

5

Application

22/02/11 Meeting Synchrone

6

Setting

22/02/11 Meeting Synchrone

48

3

95

61

7

2

• One sink/Multi source

• Connected

• Identified

• Reliable

•Asynchronous

• Spontaneous requests

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)

8

Probability Laws

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

– Problem: hitting time = O(N3)

22/02/11 Meeting Synchrone

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)

22/02/11

Meeting Synchrone 10

RW vs. RWLD

22/02/11

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)

22/02/11

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 ?

22/02/11

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

22/02/11

Meeting Synchrone 14

Full ? (Update policy)

• FIFO policy

• Rand policy

22/02/11

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

Meeting Synchrone 16

Rand Policy

• Update(e,L)

22/02/11

a b d e

a b f d g z e

Rand

Meeting Synchrone 17

Sum up

• Probability law: RW / RWLD

• Tabu Lists Location: node / message

• Tabu List size

• Update policies: FIFO / Rand

22/02/11

Meeting Synchrone 18

Tabu List in Messages (TLM)

22/02/11

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]

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

Meeting Synchrone 20

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

• Next destination ?

22/02/11

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

Meeting Synchrone 22

Hitting time (1/2)

22/02/11

Meeting Synchrone 23

Hitting time (2/2)

22/02/11

Meeting Synchrone 24

Volume, e.g., sum |messages|

22/02/11

Meeting Synchrone 25

Convergence of TLCN

22/02/11

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

Meeting Synchrone 27

Analysis

22/02/11

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

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

…

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

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

Meeting Synchrone 32

RWLD+TLM vs. RWLD (2/2)

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

22/02/11

Meeting Synchrone 33

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

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

22/02/11

34

TLCN

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

22/02/11 Meeting Synchrone

Sink

Source

∞1

Meeting Synchrone 35

Thank you22/02/11