Connected Infrastructures

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Maria Potop-Butucaru

Connected Infrastructures

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Self-stabilizing connected infrastructures

• Objectif : Choisir un ensemble de noeuds M tel que :

- chaque noeud du système est dans M ou voisin à M (couverture)

- les noeuds dans M peuvent communiquer entre eux (connectivité)

Qualité de service : auto-organisation et tolérance aux

fautes

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Model

 Id uniques.

 Indicator (eg. bandwidth , energy level, storage level)

 Local communication

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First Solution :

Maximal Independent Set

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Network

nodes

« Passive »

« Active »

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Node i

Rule 1:

Passive and Candidate(i) Change to Active

Rule 2:

Active and (not Candidate(i)) Change to Passive

Candidate(i) iff i has no neighbor j Active or i has the best indicator in its neighborhood

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MIS execution

p

t

t1 s1

v

s

p – execute Rule 1 (candidate not active)

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MIS execution

p

t

t1 s1

v

s

p – executed Rule 1 v et s – execute Rule 1

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MIS execution

p

t

t1 s1

v

s

p – executed Rule 1

s – execute Rule 2 (v has a stronger indentifier)

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Network

nodes

« Passive»

« Active»

« Bridge »

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CDS : Node i

Step 1:

Passive and CandidateBridge(i) and (not Covered(i)) change to Bridge

Step 2:

Bridge and (not CandidateBridge(i) or Covered(i) ) change to Passive

CandidateBridge(i) iff i has a neighbor j (Active) and the neighborhood of i is not included in those of j

Covered(i) iff i has a neighbor j such that

– neighborhood of i is included in the neighborhood of j or – i and j have the same neighbors and j has a better indicator

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CDS execution

p

t

t1 s1

v

s

t1 – execute Rule 1 (candidate « bridge» and not covered by an « active » node)

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CDS execution

p

t

t1 s1

v

s

t1 – excute Rule 1 t – stays « passive » s1 – can execute Rule 1

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CDS execution

p

t

t1 s1

v

s

t1 - executed Rule 1 t - stays « passive»

s1 - executed Rule 1 s - stays « passive »

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Faults

• Wrong initialisation

• Corruptions of nodes memory

• Faulty nodes and communication links

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Correction of faults

p

t

t1 s1

v

s t1 change to

« passive »

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Correction of faults

p

t

t1 s1

v

s

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Correction of faults

p

t

t1 s1

v

s t change to

« bridge »

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Correction of faults

p

t

t1 s1

v

s

- t exécute règle 2 parce qu'il est couvert par t1 et corrige son état- t1 exécute règle 1 parce qu'il est un « pont » et corrige ainsi son état

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Stable state

p

t

t1 s1

v

s

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Algorithm Complexity

 States : 3 (2 bits)

 Time Complexity: O(f(n)+n) where

O(f(n)) is the complexity of a MIS

algorithm

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Second solution :

Dominating Sets

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Node i

Step 1:

Passive and IndependentNeighbors(i) and not Dominated(i) Active

Step 2:

Active and (exists neighbor j, j Active and Dominated(i) per j) Passive

Step 3:

Passive and the same neighborhood as its neighbors and MaxIndicator(i) Active

IndependantNeighbors(i) iff i has two neighbors who are not mutually neighbors

Dominated(i) per j iff

– Neigborhood of i is included in the neighborhood of j or – i et j have the same neighbors and j has a better indicator

● MaxIndicator(i) iff i has the maximal indicator in his neighborhood

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Algorithm complexity

 State Complexity : 2 (1 bit)

 Time Complexity: n steps

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Connected Zone Covering

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Le modèle Le problème

Des solutions Les résultats Perspectives

Connected Zone Covering

Select a subset of nodes such that :

They cover the impact zone (Covering), They can communicate (Connectivity).

Gupta, Das, et Gu, ACM MobiHoc 2003[GDG03].

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Le modèle Le problème

Des solutions Les résultats Perspectives

Weak points in [GDG03]

• No self-stabilization

• No distribution

• Not optimal in memory

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Le modèle Le problème Des solutions Les résultats

Perspectives

Two solutions

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Le modèle Le problème Des solutions

Les résultats

Perspectives

To the center:

To the outside:

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Les résultats

Perspectives Sensor

Impact Zone passive

active

Notations

Outside

Inside Border

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Les résultats Perspectives

Principle : at the border

Redondant

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Principle : inside

closest to the center

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Principle : inside

Closest to the center

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Principle : extra sensors

Redondant

Connected Neighbors

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Principle : finally

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Tolerated Faults

• Wrong initialisation

• Memory Corruption

• Crashes

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Fault

Example

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Algorithm

If Outside

●

Change to red

If Border and not Redondant

●

Change to black

If Redondant and Connected neighbors

●

Change to red

If best Inside and not Redondant

●

Change to black

The best interior is the sensor closest to the center in

the intersection of two black sensors.

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Solution 2 : Distance free

If Outside

●

Change to red

Else if Redondant and Connected Neighbors

●

Change to red else

●

Change to black

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Le modèle Le problème Des solutions Les résultats

Perspectives

Results

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Le modèle Le problème Des solutions Les résultats Perspectives

• Region :

●

Impact zone : cercle of radius 40

●

Grid 25 x 25 (625)

●

Distance between sensors : 4

●

Sensors :

●

Communication radius. : 9

●

Conf. init. : aléatoire

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Results

123 sensors 115 sensors

Average coverage size

57 sec 46 sec

Average stabilization time

Algorithm 2

Algorithm 1

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cover stabilization / crash / transient faults / transient faults of only active sensors

0 50 100 150 200 250 300 350

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 time

no. active sensors

Dependant Independant

Stabilisation et fautes

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• Region :

●

Impact zone : cercle of radius 20

●

600 sensors

●

Sensor :

●

Communication radius : aleatory 5-15

●

Conf. init. : aleatory

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Results

104 sensors 80 sensors

Average covering size

190 sec 175 sec

Average stabilization time

Algorithm 2

Algorithm 1

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Stabilization

0 50 100 150 200 250 300 350

0 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198

time

#black sensors

DMSC IMSC