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Aligned Virtual Coordinates forGreedy Routing in WSNs

Ke Liu and Nael Abu-GhazalehDept. Of Computer ScienceSUNY Binghamton

MASS, October 12, 2006

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Outlines

Motivation of Virtual Coordinates System (VCS)

Brief introduction to GPSR/GFG (Geographic Routing)

Anomalies in VCS

Intuition and Design of Aligned VCS

Performance evaluation

Conclusion

IEEE MASS 2006, October 12, 2006

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Motivation of VCS

Geographic Routing Efficient for WSNs

Stateless: no state information (info of sink and path)

Localized Interactions (only info of one-hop neighbors)

GR suffers from Voids and Localization Errors

Virtual Coordinate Systems (based on connectivity info.)

Better? Based on partial connectivity info.

We show they suffer their own anomalies

Quantization Error is a factor


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GPSR/GFG: Greedy Forwarding (GF)

Greedy Forwarding(GF)


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GPSR/GFG: GF may fail

Physical Void in GF


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Distance Map Show

0

15

30

45

PhysicalDistancetoNode(21,2

0)

0 5

1015

2025

3035

4045

50

X0

10

20

30

40

50

Y

Distance Map of a physical hole


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Virtual Coordinates For Geometric Routing

Several nodes are elected to be anchors: one node per dimension;

Anchors broadcast Virtual Coordinate beacons;

Each other node forwards beacons, incrementing distance;

Each node obtains a VC based on recevied beacon values;

Distance measured in number of hops: integral value;


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Argued VCS (VCap)

3 anchors (a 3D VCS) are enough to map the physical coordinates

VC Zone can be avoided if density is high enough

VC Zone: nodes with the same VC values

VC Zones are connected with 3 anchors adapted (3D VCS)

Void (anomaly) ratio is reduced much


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Anomalies found in VCS

3D VCS is not enough to map

VC zones may be disconnected in 3D VCS

Anomaly ratio may be increased by VCS

More routing (greedy forwarding) anomalies happen


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Anomalies in 3D VCS

0 1 2 3 4 5 6

1

2

3

4

5

6

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23Z

24 25

(0 4 4)X (1 3 4) (2 2 4) (3 1 4) (4 0 4)Y

2 Units > Radio Range > 1.414 Units

(1 4 3) (1 3 3) (2 2 3) (3 1 3) (4 1 3)

(2 4 2) (2 3 2) (2 2 2) (3 2 2) (4 2 2)

(3 4 2) (3 3 1) (3 3 1) (3 3 1) (4 3 2)

(4 4 2) (4 4 1) (4 4 0) (4 4 1) (4 4 2)

Extended & Disconnected VC Zone Problems

Details can be found in previous work


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Anomalies in 3D VCS (virtual voids)

0

20

40

60

VirtualDistance(3D)toNode(1,50

)

0

10

20

30

40

50

Y

0

510

1520

2530

3540

4550

X

Radio Range 1.5 Unit

Virtual Voids

Virtual voids even without physical void


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4D VCS? or Different Distance measurement?

4D VCS was proposed too (LCR)

Anomalies in 4D VCS were found in LCR; solution requires each data

packet records each node along its path during forwarding

Different distance measurement was prosposed (BVR), Manhattan style

distance, indicated as a better solution


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Existing solutions do not reduce anomalies

0

70

4DEuclideanDistancetoNode(21,2

0)

05

1015

2025

3035

4045

50

X0

10

20

30

4050

Y

Virtual VoidsRadio Range 1.5 Unit

0

20

40

60

80

100

120

4DManhattanDistancetoNode0

0 510 15

20 2530 35

40 4550

X010

20

30

40

50

Y

Virtual VoidsRadio Range 1.5 Units

Eclidean Distance in 4D VCS Manhattan Distance in 4D VCS


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Why Anomalies in VCS?

Virtual Coordinate values are integral:

quantization error or noise increases

requiring more precise values for VCs

No discrimination among nodes in range:

forwarding dilemarequiring in range discrimination

Mapping from a continuous space to a discrete space:

less forwarding candidates

requiring continuous space


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Aligned VCS: Intuition

Anchor

1

3

2

A

B

Node A and B are different as forwarding nodes, since with different regions

of neighbors in their range.


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Aligned VCS (AVCS)

AVC of a given node is computed as a function of its VC and neighbors

VC

Simplest value: average of the neighbors integral virtual coordinate val-

ues

AVC coordinates with depth d are decided by its neighbors aligned vir-

tual coordinates with depth d 1

Original integral virtual coordinates are AVC with depth0


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AVCS (contd)

0

8

16

EuclideanD

istancetoNode(2,

8)

0 24 6

8 1012 14

16 1820

X (RR = 2.5 Units)0

4

8

1216

20

Y

VCS Forwarding Void

0

5

10

15

EuclideanD

istancetoNode(2,

8)

0 24 6

8 1012 14

16 1820

X (RR = 2.5 Units)0

4

8

12

16

20

Y

Forwarding Voids in 4D VCS Aligned VCS without forwarding voids


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Simulation

Metrics:

Greedy Ratio: how many pathes do not face any anomalies

Path Stretch: the average length of all path (both GF and CR) comapred

to optimal solution (SP)

Simulator:

NS-2: for network with less than 400 nodes

Customer: for network with 1600 or 2500 nodes

Based more than 30 networks used for each scenarios


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AVCS Performance: Greedy Forwarding Ratio

5/400 13/400 29/400 49/400 81/400

70%

80%

90%

100%

Physical (cycle) Void Size (RR=1.5 units)

GreedyRatio

GF on GeoCSGF on GeoCS with 20% Loc ErrorGF on GeoCS with 40% Loc Error

GF on 3D VCS (VCap)GF on 4D VCS (LCR)GF on 4D Aligned VCS depth 1GF on 4D Aligned VCS depth 2


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AVCS Performance: Greedy Forwarding Ratio over

BVR

5/400 13/400 29/400 49/400 81/400

30%

40%

50%

60%

70%

80%

90%

100%

Hole (cycle) Size (RR = 1.5 units)

GreedyRatio

Original BVR on 4D VCSBVR on 4D Alinged VCS depth 1BVR on 4D Alinged VCS depth 2

BVR on 4D Alinged VCS depth 3BVR on 4D Alinged VCS depth 4


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AVCS Performance: Path Stretch

5/400 13/400 29/400 49/400 81/400

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35


PathStretchtoSP(=1

.0)

Shortest PathGPSR on GeoCSGPSR with 20% Loc ErrorGPSR with 40% Loc ErrorGR on 4D VCS (LCR)GR on 4D Aligned VCS (depth=1)


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AVCS Performance: Path Stretch over BVR

5/400 13/400 29/400 49/400 81/400

1.4

1.6

1.8

2.0

2.2


PathStre

tchtoSP(=1

.0)

Original BVR on 4D VCSBVR on 4D Alinged VCS (depth 1)BVR on 4D Alinged VCS (depth 2)BVR on 4D Alinged VCS (depth 3)BVR on 4D Alinged VCS (depth 5)BVR on 4D Alinged VCS (depth 5)


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AVCS Performance: Depth

5/400 13/400 29/400 49/400 81/400

90%

92.5%

95%

97.5%

100%


Gre

edyRatio

Depth 1

Depth 2

Depth 3

Depth 4


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AVCS Performance: GF ratio with random

deployment

12 14 16 18 20

40%

50%

60%

70%

80%

90%

100%

Normalized Density

GreedyRatio

GF on GeoCSGF on GeoCS with 20% Loc ErrorGF on GeoCS with 40% Loc ErrorGF on 3D VCS (VCap)

GF on 4D VCS (LCR)GF on 4D Aligned VCS depth 1


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AVCS Performance: Path stretch with random

deployment

11 12 13 14 15 16 17 18 19 20 211.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

Normalized Density

PathStretchtoSP(=1.0

)

GPSR on GeoCSGPSR on GeoCS with 20% Loc ErrorGPSR on GeoCS with 40% Loc ErrorGR on 4D VCS (LCR)GR on 4D Alinged VCS (depth 1)


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Conclusions

Greedy Forwarding performs much better than complementary routing

phase;

Virtual Coordinates System with simple integral values create more anoma-

lies than Geometric Routing;

Aligned VCS help reduce anomalies, enhancing performance;

Geometric Routing in VCS (AVCS) can provide equivalent, or even bet-

ter performance, than geographic routing;

Further, stateless routing can approach that of stateful routing proto-

cols, such as shortest path routing.


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Thank You !

Code is available on my website

http://www.cs.binghamton.edu/kliu

Questions?


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Back up : Multiple Physical voids

1 2 3 4 5 16

40%

50%

60%

70%

80%

90%

100%

Number of Holes

G

reedyRatio

GF on GeoCSGF on GeoCS with 20% Loc ErrorGF on GeoCS with 40% Loc ErrorGF on 3D VCS (VCap)GF on 4D VCS (LCR)GF on 4D Aligned VCS depth 1GF on 4D Aligned VCS depth 2

1 2 3 4 5 1618

20

22

24

26

28

Number of Holes (Physical Voids)

AveragePathLength

Shortest PathGPSR on GeoCSGPSR on GeoCS with 40% Loc ErrorGR on 4D VCS

GR on 4D Aligned VCS depth 1


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