finding a polygon hull in wireless sensor...

Finding a Polygon Hull in Wireless Sensor

Networks

Ahcène Bounceur, Reinhardt Euler, Ali Benzerbadj, Farid Lalem,

Massinissa Saoudi, Tahar Kechadi and Marc Sevaux

Ahcene.Bounceur@univ-‐brest.fr -‐ EURO – 2015

Motivations

2

Secure site

Border nodes

Radio link

Non border nodes

Intrusion Dead baEery

Interference Failure

Explosion


Motivations

3

Secure site

Intrusion Dead baEery

Interference Failure

Explosion

ALARM

New border

Border nodes

Radio link

Non border nodes


Outline

1.  Polygonal hull in a connected Euclidean graph

1.  PHFP : Polygon Hull Finding Problem & PHVP : Polygon Hull Visiting

Problem

2.  The proposed Algorithm

3.  Simulation: Demo

2.  Material implementation of the algorithm

1.  The distributed version of the proposed algorithm

2.  Simulation: Demo

3.  Material implementation: Demo

3.  Conclusion & Perspectives

4

PHFP & PHVP

1.1


PHFP & PHVP

B

C

D

E

F

A G

H

J

Convex Hull Euclidean point set


PHFP & PHVP

B

C

D

E

F

A G

H

J

Convex Hull Connected Euclidean Graph


PHFP & PHVP

B

C

D

E

F

A G

H

J

PHFP

Polygon Hull Finding Problem

Polygon Hull Connected Euclidean Graph

Only edges of the graph can be used as connec8ons


PHFP & PHVP

B

C

D

E

F

A G

H

J

PHFP

Polygon Hull Visiting Problem

Polygon Hull Connected Euclidean Graph

THE PROPOSED ALGORITHM

1.2


Jarvis’ Algorithm (Euclidean point set)

B

C

D

E

F

A G

H


4

3


B

C

D

E

F

A G

H

2

pa(Pa , Pb , Pc) = Angle formed by edges: PbPa and PbPc N(Pc) : set of neighbors of Pc

Pa Pb Pc

pa(Pa , Pb , Pc )

1



•  Complexity: O(nh)

•  n: Number of the nodes of the graph

•  h: Number of the border nodes


The proposed algorithm (connected graph)

B

C

D

E

F

A G

H


1


B

C

A

D

G

[A]

E

F

H



1

B

C

D

A G

[A]

E

F

H


2


1 B

C

D

A

[A, C]

E

F

H

G


3


1 B

C

D

E

F

A

2

G

[A, C, D]

H


4


1

C

D

F

A

2

3

E

G

H

[A, C, D, E]


5


1

C

D

F

A

2

3

4 E

G

H

[A, C, D, E, H]


5

6


1 B

C

D

F

G A

2

3

4 E

H

[A, C, D, E, H, G]


5

6


1 B

C

D

F

A

2

3

4 E

G

H

Version 1

[A, C, D, E, H, G, A]



•  Version 1

– Complexity: O(kh)

–  k: Maximum degree of the graph

–  h: Number of the border nodes

PROBLEMATIC SITUATIONS


Boat graph


Boat graph

A

C

B D


Boat graph

A

C

D B

1 (to C) 2

P


1

3

4

5 6

2

A

B

C

D

E

F

Boat graph

7

8

9


1

3

4

2

A

B

C

D

E

F

Boat graph

4

Intersec8on


2

i+1

i

Intersection (1)

A B

C

D

i-1

1

The currently found border edge must not intersect with the previously found border edges


3

4

2

Intersection (2.1)

A B

C

1

Consider intersecZons with open intervals

and not:

3

4

2

A B

C

5

D

1


Anchor graph


Anchor graph

A

C

D

B

Formed by the edge AC and the triangle BCD


Graphe à Ancre

A

C

D B

1 (to C) 2

Two angles (PBC et PBD) having the same value à Choose the point which is near to B (ie. C)

P


Anchor graph

H

D B

E

8 3

4

5 6

F G

A

C 7

J

1

2 9

If the algorithm starts from A then the point A will be reached but not the point J !


Anchor graph

H

D B

E

8 3

4

5 6

F G

A

C 7

J

1

2 9

If the algorithm starts from A then the point A will be reached but not the point J !

1


Anchor graph

H

D B

E

2 3

4

13 14

F G

A

C 1

5

6

7 8

9

10

11

12

I

J

K

PHFP : solved? PHVP : solved?


Anchor graph

H

D B

E

F G

A

C 1

I

J

K

10

9

16 17

11

12

13

14

15

PHFP : solved? PHVP : solved?


1

i+2

i

2

i+1i+3

i+4

i+5

n

Non visited Border Nodes

Anchor graph

n-1

B

A hole

n+1

Coming back to the starZng point does not guarantee the terminaZon of the algorithm! à We have to add an addiZonal iteraZon to verify of there exists a non visited border node.


The proposed algorithm (Version 2)


Proposed algorithm (connected graph)

•  Version 1 (planar graph)

– Complexity: O(kh)


–  h: Number of the border nodes

•  Version 2

– Complexity: O(kh2)


–  h(h+1)/2: Number of the border nodes by considering

the intersection detection

SIMULATION: DEMO

1.3


CupCarbon : www.cupcarbon.com

•  A WSN design and simulation platform

•  Java API (Application Programming Interface)

à VIZOR


Simulation: Demo hEps://www.youtube.com/watch?v=7VHKW_l9juI


Simulation: Demo (100 points)

DISTRIBUTED VERSION OF THE PROPOSED

ALGORITHM

2.1


Sensor node 1. Sensor (Sensor unit) 2. Radio module (communicaZon) 3. Microcontroller ß Script (program) 4. BaEery 5. GPS 6 Mobility

1

3 2

4

1 3

2

4

1

3

2

4 1 3

2

4

5 2

TelosB


Messages & Packets

•  3 types of messages:

AC (Ask for Coordinates): Send me your coordinates

CS (Coordinate Sending): My coordinates are

SN (Select Node): You are a border node

•  Packets format:

Message AC : id | AC

Message CS : id | CS | x,y

Message SN : id | SN | x,y


The distributed version of the proposed algorithm

S3

S2

S4

S5

S8

S7 S6

S1

S1 is marked as a border node



S3

S2

S4

S5

S8

S1

S7 S6

1|AC

1|AC

S1 send a broadcast message ‘AC’ and its id



S3

S2

S4

S5

S8

S1

S7 S6

4|CS|7,7

2|CS|2,4

S2, S3, S4 and S7 receive the message ‘AC’ and send to S1 their coordinates, their id and the message ‘CS’



S3

S2

S4

S5

S8

S7 S6

S1

S1 will calculate the angles formed by a fic8ve point S1’ and its neighbors and chooses the smallest one

S1’

Minimum



S2

S4

S5

S8

S7 S6

S1

S1’

S3

Minimum

S1 will send a message ‘SN’ to S3 to inform it that it is the next border sensor, its id and its coordinates



S2

S4

S5

S8

S7 S6

S3

S1 à S3

S1 saves the id of its neighbor S3



S2 S5 à S8

S8 à S7

S6 S7 à S1

S4 à S5

S1 à S3

S3 à S4

SIMULATION: DEMO

2.2


Simulation: Demo hEps://www.youtube.com/watch?v=ojgZPlvwcMo

MATERIAL IMPLÉMENTATION: DEMO

2.3


Implementation: Demo

Sensors: TelosB / Arduino-‐XBee

hEps://www.youtube.com/watch?v=vObmCb67jg4

CONCLUSION & PERSPECTIVES

3


Conclusion & Perspectives

•  Presentation of a new algorithm allowing to determine the polygon hull of a wireless sensor network : –  Sequential version: allows to validate the theoretical concept

of the algorithm

–  Distributed version: allows the real implementation

•  Model the same problem by taking into account different parameters: detection, energy, interferences, etc.

•  We are working on: –  The GPU based simulation in CupCarbon

–  Energy Consumption of the proposed algorithm

–  Proving the optimality in number of vertices and total distance of the proposed algorithm


Thank you for your attention

Questions ?

Ahcène Bounceur, Reinhardt Euler, Ali Benzerbadj, Farid Lalem, Massinissa

Saoudi, Tahar Kechadi and Marc Sevaux

[email protected]

www.bounceur.com / www.cupcarbon.com

finding a polygon hull in wireless sensor...

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